Pre-Dominiom war when everything is pretty chill. Starfleet kinda seems fun until you realize that you have to basically do military training and all this bullshit to join and then you gotta go die in space half the time. I'd maybe just try and get a runabout or the equivalent and just sorta wander around with some pals and look at totally safe and previously explored space things. I would also open a Volcel Precinct on Risa.
Due to advanced space magic medicine, I'd run an RPG and not have to cancel every other session due to one of my players getting strep or the flu.
More seriously, I kind of turn into a mess without structure, so not having a job would be a concern in a FALGSC situation. Traveling with a preplanned itinerary would probably be cool, and I'd get to experience a lot of alien cultures and beautiful sights.