I have a 10 year old Jacksonville and The Beaches streetmap that shows the names of the neighborhoods:
Should the photo be deleted for whatever reason, please DM me.
Everything east of Selva Marina Drive is VERY nice and you don't have to worry about crime at all. We stayed in an oceanfront vacation home/condo recently in The Bluffs area and the owner who was not at home when we arrived (around 9 p.m.) left the entry door unlocked. It didn't seem to bother her at all. I have no crime statistics, but I'd say there's almost zero random crime.
Other "rather" nice parts are Selva Linkside, Selva Lakes, Seaspray and Saltair. Never heard about much crime there, either.
Then there's the Mayport corridor, which I would definitely avoid. Although the city is trying to make it nicer and safer, it's still a place I prefer to pass with the doors locked.
I haven't been in the neighborhoods west of Mayport Rd, so I can't tell you anything about them.
Connie