As much as I absolutely LOVE space/astronomy, I would choose Time Travel in a heartbeat.
Only someone who actually knows what makes up most of the visible universe will realize how BORING and EMPTY it is.
Will you use FTL travel in an attempt to discover more life? You know, the odds of which are so astronomically low that you will have to thoroughly check a billion planets before you have the vaguest chance of finding anything?
Or will you use it to take photos/videos of what Hubble has been basically doing since it was made, except now you get close-ups! Or will you use it to orbit far-away planets/stars, or land on the surface of planets/moons? After your 50th trip to yet another world encased in dust, ice, gas or volcanoes, what will you do next?
Seriously, if people are expecting Star Trek that's the last thing that's going to happen. There's a 99.9% chance you'll see yourself get bored within a matter of weeks, find yourself floating in some distant galaxy and asking your friend "sooooooo, where to now?" and he'll most likely reply "Well we've seen just about everything from black holes to quasars, it takes millions/billions of years for anything interesting to HAPPEN. I'm bored as fuck."
Meanwhile with Time-Travel you would actually be able to find out IMMENSELY important things that people would literally kill themselves (and I mean literally) to find out. And not even with an intent to change the future, but just KNOWING things that nobody else knows (or no longer believes in) would be so satisfying! I want to see rewind back to when Jesus was allegedly alive, I want to see who shot JFK, I want to see where mankind will be in 500 years! That would be a thousand more times more interesting than teleporting around the universe observing shit -_-
Yes, it's dangerous. But you have to establish exactly what kind of Time Travel we're working with here. Are we working with a single timeline, where if you change something in the past then the future of that timeline will be altered?
Or are we working with multiple timelines, where everytime you time-travel you simply enter another parallel universe and no matter what you do you can't change what happens to your OWN universe, you only end up changing the future of an alternate universe?
In any case, I would make sure to take someone extremely intelligent (when it comes to staying secret) taking me along on the journey. Because I know there's a fairly high chance that I'll end up screwing-up something with my very presence, even if I just want to observe stuff.