Trying to plan an 8 day trip in March, need suggestions.

My wife and I are planning to go to Italy in March from the US. We want to see the sights and do the things and don't know where to start(a travel agent is after this.)

Budget ~9000usd(not including airfare)

Things we want to do - eat the pastas, eat the pizzas, taste the olive oils, drink the wines.

Touristy stuff - Tour the Colosseum, visit the leaning tower of piza, maybe go in a canal in venice. Etc etc. We want to visit 4-5 different cities.

Non touristy stuff - idk? We like to do some stuff off the beaten path as well.

We are not concerned with the beach or coast.

Open to suggestions, where should we go, where do we NEED to eat. Where should we stay? Where should we fly in/out of?