I live in the greater Cincy area and work downtown near the stadium, so here's the scoop:
Parking will run from $3.00 - $50.00...depending on where you park
You can park about 5 blocks from the Stadium in several places (At the Westin Hotel, Fountain Square Parking Garage and pay about $3.00 - $10.00. Make sure you are there at least 2-3 hours before the game! Those go pretty fast. No tailgating allowed at those places!)
There are public and private spots within 3 blocks of the stadium which charge $15-$50 that allow tailgating. Of course, the closer to the Stadium you get, the more expensive it is. The Parking Pass only lots tend to sell out fairly quick, not sure how much those are. You can go to the Browns website to see about those.
I'll be at that game! Will be lots of fun!!! :)