Maybe it's because I live in Colorado, but I instantly associate it with the ritzy ski town. I think of it as a posh location name for a little princess, similar to Paris.
I think the exact same thing because I live in Colorado as well. To top it off, I know a girl named Aspen who seems like she could live in Aspen. She's a little snobby and such. Not my favorite name. Also, the first syllable just makes me really dislike the name.