There are no "real" racetracks in the state of RI. The closest tracks would be Seekonk Speedway in Seekonk MA and Thompson Speedway in Thompson, CT. Seekonk has a Friday night youth division with a couple of different classes, and Thompson has its own "mini" track designed for 1/4 midgets. I'm not sure of the age ranges or details but their respective websites (www.seekonkspeedway.com
) will give you plenty of info.
As for go carts - the only places in the general area with good, fast karts are Tri State Speedway (www.tristatespeedways.com
) in Dudley, MA, right over the CT border, and F1 Boston in Braintree, MA (just south of Boston - www.F1boston.com
). I believe they both have leagues available. Super fast karts and I get my butt kicked every. single. time.
The only other go cart tracks in the area are the type that have mini-golf and batting cages attached.
Hope that helps and best of luck!!