In Jax I would recommend a few places.
Breweries/Tap Rooms: Green Room (Jax Beach), Intuition Ale Works, Bold City, and Brewer's Pizza (Orange Park), and Engine 15.
Beer Bars: Kickbacks and the various European Streets.
There are two neighborhoods here in town where you can hit a few different locations in an afternoon or evening easily.
Green Room, European Street, and Engine 15 are all very close to each other in Jackonsville Beach. Intuition, Bold City, & Kickbacks are all quite close to each other in Riverside. Kickbacks is a top notch beer bar. Their tap list is extensive and the food is quite reasonably priced. If you want a taste of their tap list, I'd recommend downloading their iphone or android ap.
On Saturday, June 16, Green Room is celebrating its first anniversary with a pig roast and a release of bourbon (Marker's Mark) imperial stout.
I'm happy to offer any further information or suggestions in regards as to what to do in town.
Websites:Bold City -
http://www.boldcitybrewery.com/Engine 15 -
http://www.engine15.com/European Street - europeanstreet.com/
Green Room -
http://www.greenroombrewing.com/Intuition -
http://www.intuitionaleworks.com/Kickbacks -
http://www.facebook.com/kickbacksgastropub