I live right off of 183 myself. The good thing is, it's close to the airport so there are a lot of decent places to stay. If you head west from the stadium on 183, you'll head towards the airport. You should pass roads Carl Rd., O'Connor, MacArthur, Story, Beltline and then Esters. On the intersection of 183 and Esters (less than 10min from the stadium) are a number of places to stay, including a Holiday Inn, AmeriSuites, Drury Inn, LaQuinta, Super 8 and a Best Western, all at that intersection.
Don't know if these are the cheapest or the best, but it's a starting point, and it's very convenient. I only live 1 block from that intersection, so I should know.