[Opinions] Well, since you asked... :)
I have a list:
Don't like:
Eliza (too harsh)
Elisa
Liza
Lisa (a little dated to me)
Betty
Betsy (this one is ok, I guess)
Elsa
Bess
Bessy/Bessie (sounds like a cow to me, no offense intended)
Like (starred are faves):
Beth (in certain cases, sounds shy to me)
Liz*
Lisbet/Lisbeth*
Lissa
Lissie/Lissy*
Bet
Lizzie
Ellie*
Ella
Elle
Lisabet
Liss/Lyss
Elsie
Libby*
Yet much like LM Montgomery's character (can't remember which book off the top of my head), if Elizabeth was my name, I think my nn would change from day to day depending on my mood. Some days I feel like a Lizzy, and some days, I'm just a Beth. :)