I would head to every star that could sustain life, each with a reasonable habitable zone where planets might arise, or where we know planets already exist. Why? To answer, once and for all, the age old question: are we alone in the universe? Because, hey, if you've got an FTL ship and you don't have to worry about time dilation, fuel (a problem for current propulsion models), and so on; if you've got that, then why not head out on a 30 second trip to Alpha Centauri and see a binary star close up for the first time ever, looking for that one little planet that might very well put truth to the words of countless science fiction authors who have proposed life around our binary cousin and in the universe (trinary, if you want to get darn specific)? Why not see the check every potentially habitable rock for signs of intelligent life and come back with an answer, laying to rest Fermi's Paradox and establishing into law (or modifying) Drake's equation?
That sounds like a fantastic way to spend a few days in an FTL spaceship to me. What about you?
So, if you had a spaceship with faster-than-light capability, minus all the negatives typically associated with a realistic vision of FTL, where would you go and why?