Don't try to enter all those cities. Total the box 18 & 19 amounts, from your W-2s, and make only one entry in box 18 & 19. Type GE (generic city) in box 20. That will allow you complete your Ohio return.
Don't try to do RITA in Turbotax. you'll be doomed to frustration and failure. Do it by hand or at the RITA web site. http://www.ritaohio.com/
You only have to file city return(s) for the city(s) you lived in , not every city you worked in.