I like the name Avery Elizabeth.. as others have said it flows nicely. Depends a bit on the last name though since for most of the time we don't use middle names!!
I think both Avery & Payton are pretty names, but I prefer Elizabeth as a middle name... probably just more because I'm familiar with it. I also prefer 1-2 syllable names to go along with 3 syllable names. I'm kind of a freak when it comes to baby name rules for myself though.
I also like the way Avery Elizabeth sounds, very pretty!
My blog about helping my deaf son learn to listen and speak.