Nice to meet you to. At least in the online sense of meeting!
It makes sense to explore a new city with an open mind--so perhaps vague is exactly what you ought to be! My favorite places are pretty diverse. I have a favorite English-style pub that's not too far. I love to just wander around and visit random art galleries--no particular favorites, just the fact that there are so many and there's always something new to see. You can't go wrong with the New York classics: Central Park, Times Square...even if you just go once so you can see it for yourself.
Unfortunately, yes--the elevator misbehaves on a regular basis. It seems to almost have a somewhat perverse sense of humor about it--choosing really bad times to leave you stranded some place other than where you want to be!