Yes the traveling serious about being competitive teams are expensive. But each city should have a league to play in that's very affordable and its typically no travel.
Baseball, soccer, football(tackle and flag) and basketball are the big ones in your are you should be able to find easily.
Your local citys website should have the info
EDIT:
http://www.uaoh.net/egov/apps/document/center.egov?view=item&id=2967
just a quick google search shows a few sports for UA
Basketball is 95$
All the others don't show a price, I am assuming it tells you the price when you do the online registration