Gateway is on the Westside. As already mentioned, it's an outdoor range.
Bullseye, also mentioned before, is an indoor range that is more in town. Some would call it Southside, some east. If you look at a map, it's at Atlantic and University.
I belong to both places, so obviously I like them. Both places have their detractors as well.
There's also a place on Beach Boulevard called
Gun Gallery. I prefer Bullseye to Gun Gallery because there are more lanes, they are better lit, and there's more room behind the lanes.
There are a couple of outdoor ranges around St. Augustine.
Ancient City Shooting Range (I used to be a member) is pretty nice, but it's expensive. There's also an FOP range (I don't know their website, if they have one).
I've never been to the 2nd Amendment range mentioned above, but I hear nothing but good things about it. There are a couple of indoor ranges that are supposed to open in the near future.
What part of town will you be working in? That might help you decide where you want to live and where you want to shoot.
I live in Orange Park (just south of Jax on the west side of the river) and work on the Southside (which is why I belong to two ranges).
If you want more info/opinions, feel free to PM me.
And welcome to town!