I recently did a post on Davos Seaworth's whereabouts during Balon Greyjoy's rebellion. I'd like to do something similar for Oberyn Martell.

Mapping Oberyn Martell's Whereabouts

Early Years

• Oberyn was born in 257/258 AC and was later fostered at Sandstone (House Gorgyle)
• He traveled with his mother and sister Elia looking for potential marriage candidates visiting numerous castles (and ultimately Casterly Rock)
• In 274/275 AC Obern was found abed with the paramour of Edgar Yronwood and killed him with a poisoned blade in the duel

If interested: Elia's Suitors: Obery & Elia Martell's Quest to Casterly Rock

The Sand Sneks

• Obara (271/272 AC in Oldtown)
• Nymeria (274/275 AC in Volantis)
• Tyene (276/277 AC on a Septa)
• Sarella (280/281 AC on a Summer Islander captain)
• Elia (285/286 AC on Ellaria Sand)
• Obella (287/288 AC on Ellaria Sand)
• Doreah (291/292 AC on Ellaria Sand)
• Loreza (293 AC on Ellaria Sand)

I think we can use the ages of the Sand Snakes/some of these quotes to map out a napkin math-esque outline of his general whereabouts.

Oldtown

Its likely that Oberyn headed to Oldtown in 271/272 AC:

He had studied at the Citadel, going so far as to forge six links of a maester's chain before he grew bored. -ASOS, Tyrion V

He likely stayed for a few years (forging chain links) or returned after his "exile" to pick up Obara (who he fathered on an Oldtown whore).

"Exile"

It seems likely that at this time Oberyn returned to Oldtown and picked up Obara

The Red Viper went to Oldtown, thence across to the narrow sea to Lys, though none dared call it exile. -TWOW, Arianne I

Lys (after 271 (likely) and before 274 AC)

Sometime after forging 6 links/possibly having Obara, Oberyn headed to Lys, where he likely studied poison with the Alchemists (Tears of Lys/Strangler/Manticore Venom) before joining up with the Second Sons:

He had traveled in the Free Cities, learning the poisoner's trade and perhaps arts darker still, if rumors could be believed. ... He had soldiered in the Disputed Lands across the narrow sea, riding with the Second Sons for a time before forming his own company. -ASOS, Tyrion V

Volantis (274/275 AC)

It seems Oberyn was then in Volantis at some point around 274/275 AC seeing as that is when Nymeria was born upon a Volantene noblewoman:

but Obara's mother had been an Oldtown whore, whilst Nym was born from the noblest blood of old Volantis. -AFFC, The Captain of the Guards

Which is interesting to say the least that a noblewoman of Volantene blood got knocked up by Oberyn in 275ish AC and Steffon Baratheon couldn't find a suitable one for Rhaegar in 278 AC

Return to Westeros

Once Oberyn returned from his "exile", I assume he spent plenty of time in Dorne, but he did leave at least on several occasions:

The Reach (276/277 AC)

Its possible that Oberyn then returned to Westeros as he fathers Tyene on a septa in 276/277 AC in the Reach which also coincides with the undated tourney that Oberyn crippled Willas in:

The Dornishman did not react as expected. "I had a letter from Willas not half a year past. We share an interest in fine horseflesh. He has never borne me any ill will for what happened in the lists. I struck his breastplate clean, but his foot caught in a stirrup as he fell and his horse came down on top of him. I sent a maester to him afterward, but it was all he could do to save the boy's leg. The knee was far past mending. If any were to blame, it was his fool of a father. Willas Tyrell was green as his surcoat and had no business riding in such company. The Fat Flower thrust him into tourneys at too tender an age, just as he did with the other two. He wanted another Leo Longthorn, and made himself a cripple." -ASOS, Tyrion V

and:

Her mother had been a septa, and Tyene had an air of almost otherworldy innocence about her. -AFFC, The Captain of the Guards

and:

Arianne Martell had crossed the Mander once, when she had gone with three of the Sand Snakes to visit Tyene's mother. -AFFC, The Queenmaker

The Stormlands (278 AC)

Due to the conflicting info about the tourneys at Storm's End, I think either there were two tournaments that Oberyn attended one right before Lord Steffon died and another in honor of him afterward:

• Mention #1 (unhorsed by Rhaegar)

"When he was young, His Grace rode brilliantly in a tourney at Storm's End, defeating Lord Steffon Baratheon, Lord Jason Mallister, the Red Viper of Dorne, and a mystery knight who proved to be the infamous Simon Toyne, chief of the kingswood outlaws. He broke twelve lances against Ser Arthur Dayne that day." -ASOS, Daenerys IV

Unhorsed by the champion Barristan Selmy:

Sole champion of Lord Steffon's tourney at Storm's End, whereat he unhorsed Lord Robert Baratheon, Prince Oberyn Martell, Lord Leyton Hightower, Lord Jon Connington, Lord Jason Mallister, and Prince Rhaegar Targaryen. -ASOS, Jaime VIII

Oldtown (280/281 AC)

Sarella/Alleras was born in 280 AC and while it isn't confirmed that she was born in Oldtown, I think its possible for a few reasons. Her mother was a trader who frequented the city:

Alleras smiled back at him. "I only buy for friends. And I am no lord's son, I've told you that. My mother was a trader."

Leo's eyes were hazel, bright with wine and malice. "Your mother was a monkey from the Summer Isles. The Dornish will fuck anything with a hole between its legs. Meaning no offense. You may be brown as a nut, but at least you bathe. Unlike our spotted pig boy." He waved a hand toward Pate. -AFFC, The Prologue

and unlike Obara (whose mother was a whore there), she loves the city:

Nym laughed. "Yes, she wants to set the torch to Oldtown. She hates that city as much as our little sister loves it." -AFFC, The Captain of the Guards

Tournament at Harrenhal (281 AC)

We know Oberyn was present at the Tournament of Harrenhal as he danced with Ashara Dayne:

The crannogman saw a maid with laughing purple eyes dance with a white sword, a red snake, and the lord of griffins, and lastly with the quiet wolf . . . but only after the wild wolf spoke to her on behalf of a brother too shy to leave his bench. -ASOS, Bran II

Robert's Rebellion (282-283 AC)

When asked about Oberyn's location during Robert's Rebellion, GRRM had this to say:

[Where was Oberyn Martell during the rebellion?]

GRRM: Good question. Offhand, I don't recall the answer. Maybe in Dorne, maybe across the narrow sea with a sellsword company. I'd have to check my notes to be certain. -SSM, Various Questions Concerning Tywin, Oberyn, Gregor, The North and Sansa: 15 April 2008

So its possible that he stayed in Dorne or was off with a sellsword company (we do have knowledge that he formed his own company, but we don't know when, it could have been back around when he fought with the Second Sons.

We do know that at one point he did try to raise Dorne for Viserys:

"Is it true he tried to raise Dorne for Viserys?"

"No one speaks of it, but yes. -ASOS, Tyrion VI

Post Robert's Rebellion

Braavos (~285 to 289 AC)

He was in Braavos in order to sign the marriage pact for Viserys/Arianne:

"It is a secret pact," Dany said, "made in Braavos when I was just a little girl. Ser Willem Darry signed for us, the man who spirited my brother and myself away from Dragonstone before the Usurper's men could take us. Prince Oberyn Martell signed for Dorne, with the Sealord of Braavos as witness." She handed the parchment to Ser Barristan, so he might read it for himself. "The alliance is to be sealed by a marriage, it says. In return for Dorne's help overthrowing the Usurper, my brother Viserys is to take Prince Doran's daughter Arianne for his queen." -ADWD, Daenerys VII

Balon's Rebellion

• Unlike the other regions, The Dornish do not seem to have been involved in putting down Balon's Rebellion

Rarely Leaves Dorne

"No one speaks of it, but yes. Ravens flew and riders rode, with what secret messages I never knew. Jon Arryn sailed to Sunspear to return Prince Lewyn's bones, sat down with Prince Doran, and ended all the talk of war. But Robert never went to Dorne thereafter, and Prince Oberyn seldom left it." -ASOS, Tyrion VI

and:

"He left you to rule in Sunspear when he took himself off to his Water Gardens, did he not?"

"To rule? No. He left his cousin Ser Manfrey as castellan, old blind Ricasso as seneschal, his bailiffs to collect duties and taxes for his treasurer Alyse Ladybright to count, his shariffs to police the shadow city, his justiciars to sit in judgment, and Maester Myles to deal with any letters not requiring the prince's own attention. Above them all he placed the Red Viper. My charge was feasts and frolics, and the entertainment of distinguished guests. Oberyn would visit the Water Gardens twice a fortnight. Me, he summoned twice a year. I am not the heir my father wants, he has made that plain. Our laws constrain him, but he would sooner have my brother follow him, I know it."-AFFC, The Soiled Knight

and:

Oberyn was ever the viper. Deadly, dangerous, unpredictable. No man dared tread on him. I was the grass. Pleasant, complaisant, sweet-smelling, swaying with every breeze. Who fears to walk upon the grass? But it is the grass that hides the viper from his enemies and shelters him until he strikes. Your father and I worked more closely than you know … -ADWD, The Watcher

which would make sense due to the fact that the youngest 4 Sand Snakes are all with Ellaria.

Oberyn was a well traveled man who answered to no one. I hope we get a bit more information on where he was/what he was up to during his time in the free cities, during Robert's Rebellion, his own sellsword company and the secret pact.

Let me know if I missed anything.

TLDR: An outline of Oberyn Martell's known locations throughout his life.