If you must stay in Omaha, be prepared to leave for the game at least 2 hours in advance - and that will get you to the gates with a few minutes to spare.
Recommendations:
Assuming that you want to stay in a higher end hotel, stay at the embassy suites downtown. It has a very nice interior atrium and the rooms are quite nice. The hotel also has a restaurant and bar. You can also get a very good suite there if you want to spend a little more. Most importantly, the hotel is across the street from the Old Market.
The Old Market is the downtown historical area with quaint shopping and what amounts to Omaha's nightlife scene. There are quite a few bars that will be full on most Friday nights including: Billy Frogs, The Dubliner, the French Underground, M's Pub, and such. Just walk around, they are all within about the same 4 block square and many have outdoor patios. If you want something really unique, get a taxi and take it up to the Crescent Moon. Its about 2 miles West of the downtown area and has a great atmosphere. There also have many many exotic foreign beers on tap (makes Old Chicago look like an Applebee's). The downstairs area has an authentic German bar that serves beer out of glass boots - just don't break it, they're $50 bucks each.
Leave for the game at least 3 hours before. Preferably 4+ hours early so you beat some of the traffic and you have time to bar hop and go to the book store. Make sure to go to Sandy's and get and "Elk Creek" and then to Duffy's for a "fishbowl." Otherwise Bisonwiches has excellent sandwiches and beer specials. Make sure to try a Runza too.
Directions: Go West from the hotel to 13th street, take a right (North). Go about 5 blocks to Cass Street. You'll see signs pointing to interstate 480 South. Take a left (West) on Cass and this literally runs strait into 480 South. Take 480 South to interstate 80 West and go to Lincoln. Get off on the downtown exit and just drive until you hit downtown. Can't help with the parking, we have reserved spots for our cars since before I can remember. There are quite a few places around the outskirts of downtown for $10 - $20 i believe.
Hope this helps
Brad