This is a great thread idea and quite a challenging question really, something to really think about.
With the rules set in play that I can not change the past, or do anything to effect the future, that does take some of the fun out of it. I think if the rules were slightly different to where you could go to the future, find out the winning lottery numbers for a given date, and then come back and play them or something to that effect, just about anyone would do that. The temptation to not do something to better yourself would simply be too great. I could see someone going to the future and seeing some kind of technology that does not yet exist, and then using that idea to get rich in the present. It could be something as simple as one of the items sold on infomercials like the Snuggie, Eggies, The Gator Grip, or some kind of odd thing like that-that makes you a millionaire over night almost.
Still, it would be really cool to see the future and how far man advances in say another 1500 years. What if you did go into the future that far though, and you found out that something biblical took place or something? Like what if you showed up in post-rapture society where the second coming of Christ has just occurred and the whole world is going to hell? That would be fucked up!
I guess since I couldn't change anything, I could only observe, than I would choose to go to the past. Arriving at a post-apocalyptic reality wouldn't be too much fun. If I went to the past, at least I could see the stuff I've always been fascinated by in history. I would go see the Parthenon, I would LOVE to see ancient Rome at it's heights, or ancient Egypt at it's heights. Maybe a trip to medieval times would be cool, or as someone else mention, go all the way back to the time of the dinosaurs. Even to go back just to the post WWII America and see how "Leave It To Beaver" America really was would be interesting, or go to the 60's and see what Woodstock was really like. Go back to the Kennedy assassination multiple times to view it from multiple places and see if there really were guys behind the fence by the grassy knoll, or go to the book depository where Oswald supposedly shot Kennedy and see if he shot at all? Find out who really did it, just for your own piece of mind. Go to the site of the Roswell crash and see if aliens really did crash on Earth, or if it was just a weather balloon? I guess the possibilities are almost endless, and it would be a lot more fun in retrospect considering the circumstances and rules, to go to the past over and over.