What all can you do with a Private Pilot License?

I saw a video on YouTube where a guy and two friends flew for a trip to New York from Miami in a Cessna... So, say I have my PPL. Could I just pack up and fly to wherever I please? What else do you have to consider... Rental fees and fuel I'm guessing, but what else?

Here a few scenarios that I would like to do in the future...

1. One of my ex girlfriends who moved away lives in St. Louis and I live in Alabama. I fly a Cessna there and stay for 2/3 days then fly back
2. Say I want a quick vacation. Me and a friend or two fly to the Bahamas for about a week then fly black.

Are these scenarios possible, and if so, so much would it be?

P.S., do Cessnas have storage for suitcases? And will amount of people and suitcases affect the weight limit?