I suggest you look into the Mandarin Area or Julington Creek. Ponte Vedra is the "posh" part. Stay away from downtown (although they got brand new condos out there) and anywhere close to Moncrief. I wouldn't want to be in Springfield either even if they are "revamping" (great cultural place though - lots of really really really old houses). San Marco is a better "cultural" place but it is also pricey.
The westside is okay around Oakleaf Plantation and surrounding neighborhoods but unless you're working in downtown or NAS Jax, it is a far drive with traffic galore. South of that is Fleming Island which is a cool place - but also far.
Southside is okay and the beaches are cool too - especially San Pablo area.
All in all, I find Mandarin the best place in town - easy access to everything - Southside workplaces, Downtown, even Clay County and St. John's county is not far. It's a zip to go to the airport and a quick hop to I-95 to go visit people in Orlando and Tampa. And the beach is close by. And the house prices are reasonable.
I might be biased though, so take it as a personal preference and not a professional one.
Dr. Rossi is the greatest reptile vet in town.
Blazing Reptiles is a cool reptile store.
Mike Cavanagh is the ASF guru.
I think that's all you need for your pets.
Oh, I forgot the point of the post - I'm from Jacksonville as well!