L.C.
There is a pottery place in East Greenwich that is fun (I think there is one in Barrington too - but not 100% sure.) Chuck E Cheese in Warwick. Lizzy's Enchanted Creamery in Cumberland, check the local libraries for story times (and they have puzzles and other toys to play with in the children's rooms). Regal Reptile's in Prov suppostedly has like a reptile zoo (but I have never been there). IMAX (depending on what movies they have). City Park in warwick has a good playground, so does Slater Park in Pawtucket. Borders can be hours of fun for me - LOL - and my little one loves to look at books too (there might be story times there too).
Check out kidoinfo.com - they have lots of things listed on their calendar. :)
Good luck! and Have Fun.