There are fine hotels on both sides of the river, having said that, I would suggest staying in NKY- Newport is great. There is a lot more going on in NKY than Cincy for pre and post game activities. Check out the site www.newportonthelevee.com for more information (and go to tourism information, for further listing of hotels etc.)
The most affordable and nice hotel is probably the Comfort Suites-Newport, where you can get a room for around $100, the others tend to be more unless you get some deal. It is located w/in a short walking distance to Buckhead Grill, Joe's Crabshack and Don Pablos- all of which have outdoor patio seating with great views of river / cincy skyline. At just a little longer walk, is Hooters and another bar which are on the river. There is a TANK bus shuttle that goes along this stretch which will take you directly across the river to the stadium for $1 each way. No need to drive, park the car, drink and be merry. The bus runs until 10 pm on weekdays or until 20 min after the game is over and until 12pm on weekends.
If you are more budget minded, the least expensive motel near the action in NKY is probably the Travelodge- its w/in walking distance to Newport on Levee and even accross the bridge to the staduum.
If you have any further questions just ask.