One of the PhD offers is from a new university belonging to a very reputed university system. I like the professors that I met. I haven't met the professor in the other university that's offering me a PhD. It is old and well-established. The location sounds more fun than the first one, which is in a small town in the west. I'd feel bad about rejecting any one of them since they have both been so nice and encouraging. Will that impact my future career and chances of getting a post-doc or job there?

That's a good question I also want answered too as I'm in same position as you! I've been told that it doesn't matter on the uni so much but check the dept and supervisor! However I still think the uni must count towards something!

I would also like to know if you accept one position is it really bad to change your mind if you haven't started the project yet? How often does it this happen? Is it frowned upon and will it affect your career prospects?

Thanks Zebedee.
I am currently in a 2nd tier smaller university but my research is not bad.
Yes, definitely look at how friendly and scientific the dept. is.