Unusually for a new ground, it's closer to the city centre than the old ground. It's still a good 20 minute walk from the station though. If you're driving over then don't even think about parking at the ground though unless you want to be stuck for ages after the game. If you arrive early enough you'll be able to park in the Brickmakers car park, otherwise the area around the ground is residents parking only. Street parking is available a bit further away, and two possible areas are marked on the pub map below. The area around the Boulevard is good for getting away after the game, while somewhere on or off Princes Avenue is handy for the best pubs.
A couple of the pubs near the ground, the Brickmakers and the Three Crowns, are apparently ok for away fans. Further up Walton Street from the Brickmakers, the New Walton Club allows away fans in for a small fee. Once in you'll find that the beer is cheap and that they do food. I'd though recommend heading to Princes Avenue. There's a number of decent pubs, but far and away the best is PAVE, which has a good range of cask ales as well as a selection of bottled foreign beers. They also have a fairly extensive food menu. It's a 15 to 20 minute walk from here to the ground.

If you're going over by train you may prefer to do your drinking in the city centre, in which case the Rugby Tavern is an option. It's a Sam Smiths pub, which means it's cheap, and they have a pool table. On the other hand it's basically a taxi job to the ground. There are a number of pubs by the station, which means they're just about within walking distance of the ground. One of them is not surprisingly a Wethersoons, however it's not one of the better Spoons. You'd be better off going to the Ebenezer Morley, a Spoons clone directly over the road. Another option would be to jump in a cab up to Princes Avenue.

All the pubs mentioned are marked on the map below, along with a few others.

Pub map
Football Ground Guide
Hull City official site