Unless your hotel is running a shuttle to the game, you'll either need a rental car or a cab.
I'd recommend the rental car because Jacksonville is a very spread out town. Most of the things "to do" are in little pockets all over the place.
If you end up driving to the game, there are tons of places to park near the stadium. There should be people working the parking lots and directing traffic. Furthermore, downtown Jacksonville has over 14,000 parking spots. Whether you're on the street or in a lot, you'll be OK as far as finding parking goes.
As for which bars to go to, check out this local blog:
You don't have to go to everything listed, but it has some good reference points. If you have a car, I recommend driving (1 or 2 miles from downtown) to Park & King District. Tons of bars, very few clubs, tons of beers on tap. There's also an array of good restaurants around there. (In the map above, I'm referring to the area where Rogue, Loft, and Garage is.)
For food, I'd try:
Pele's Wood Fire (steak, seafood, pizzas, Italian). There's also the new Black Sheep Restaurant which is a few blocks away from Park/King in 5 Points.
In San Marco, I'd try AIX or Taverna.
The restaurants listed have great alcohol lists.