Define "area". Dodger Stadium is in an eclectic neighborhood that's not really touristy. Your best bet would probably be to stay a little farther out like Pasadena or Burbank and drive over. Depending on traffic and time of day, that could be 30 minutes or 2 hours.
Mac is right - the area around Dodger Stadium is pretty "eclectic". It's near Echo Park, a predominantly Latino neighborhood that over the past few years has been getting gentrified by hipsters. Along with Silverlake, it's kind of the Brooklyn of LA.
There's a bar that I go to a lot called Short Stop, which, if you can't tell by the name, is a Dodger bar, but I think that's only on gamedays. I've never been there for Dodgers games, but it's pretty hoppin' on most nights, but again, filled with hipsters. Depending on your age/scene, it may or may not be for you.
Do you have a rental car? That'll make it a lot easier getting around. Stuff in the area will probably all be Dodger-related on a Sunday, but there are some pretty cool music venues in that area. One of my favorite breakfast spots, Brite Spot, is right over there. Might make some decent pre-game/hangover food before you start scarfing down Dodger Dogs.
Macanudo and DeadHead are correct. There are no real hotels or bars within walking distance to the ballpark.
Your best bet is to have a rental car. If you get a hotel in downtown LA, then the commute will be short (15-20min). I would recommend doing your pre-party tailgaiting in the parking lot, or just get to the park early and start downing the brews inside the park while taking in pre-game warmups.