Greetings,
Non Trolling Jags season ticket holder (by way of Boston)chiming in. For those staying close to the stadium, Downtown Jax is pretty weak but the Urban neighborhoods around downtown are pretty cool for breweries,Bars and restaurants. Riverside (just west of DT) more for bars/casual dining and a younger crowd, and San Marco just south of DT(across the river) has a very nice small town center and is more upscale dining / cocktail bars but does have a cool brewery in AArdwolf.
There is not much near the stadium but Intuition Ale Works is an excellent brewery and has good food as well. Note, An upscale steakhouse just opened up DT after a massive renovation of an old bank--Cowford Chophouse and also has a great roof top bar with nice views .It is across from the Hyatt which is the large hotel relatively close to the stadium.Mortons is in the Hyatt but if going expensive, I recommend Cowford.
If you prefer to stay near the beach, there is a nice town center that is split between Atlantic Beach/Neptune Beach that has a decent amount of Bars( including the referenced Pete's) and restaurants.