Take a tip from the professionals, there is always a budget but you have fans and business want to connect with them. Towels are kept and brought back to the game, and used around the house. That kind of multiple impressions with your fans means something to companies. Plus match your team's slogan with a local companies passion and quickly the price of a towel giveaway goes down tremendously. While we can help silkscreen, that's another point of local contact that you can use to keep you costs down. Many times the local t-shirt printer is also a big supporter of your team, and will cut you a deal to put his name on the towel too.
Of course, summer planning for fall use helps tremendously too. Give a person the ability to fit in a job rather than crashing the schedule, you will always be greeted with smiles and the best price.