Am I legally allowed to hang out with a 15 year old?

OK, so I'm a 21 year old male and I was attending the Harry Potter 6 premiere where I met this girl and we just began talking. Later on, I found out she was 15 which was somewhat of a shock but it turns out we have a lot in common so I didn't really think there was anything wrong with continuing to talk with her. We both like to read comics and play video games. Anyway, she said she doesn't go to museums much and she wanted me to take her to the Metropolitan Museum of Art. I said OK but after I decided to just look up these "age difference" questions and it seems like the popular consensus is: the guy is looking for and no good things will come out of it. Well, let me just say I have no intention of wooing her, I know the law and I have no intention of trying to manipulate her, in fact, if you forced me, I probably won't be any good at it. I asked my friend (who is 19) and she said I had nothing to be afraid of. In any case, I am just taking to the museum and that is all, like two friends hanging out but I'm afraid that people will misconstrue this and will try to get me arrested and I have no criminal record so I don't want to do something that other people will yell at me for. If the general consensus of these answers is that it's a bad thing to do than I will not do it. This is just not a thing to go to jail for.