Depends on your interests.
A walk along Benefit Street is very picturesque. You have a view over downtown and the street is full of amazing colonial, federal, and victorian style houses. There's a neat park that overlooks the city on Congdon street that is a bit of an unknown treasure. Very restful. Great place to chill out with a book, or even take an acoustic to play.
RISD museum is great if you're into art and sculptures, etc. There can be some challenging/confronting pieces in there sometimes too.
There's a chauffered dine around. You choose six restaurants from a bunch of premier eateries and enjoy featured menu tastings all evening long.
Federal Hill is a mile-long string of italian restaurants with some bars and art galleries in between.
Thayer St and Wickenden St are both well worth visiting (and often). Lots of college kids there, but it's full of eateries, bars, coffee shops, etc. and some fun eclectic shops. There's an awesome falafel/gyro place called east side pockets on Thayer.
There's two great breakfeast or brunch restaurants well worth checking out. Julian's and Nicks on broadway (both are on broadway in fact but several blocks apart). Julian's is very eclectic - the tatts and body art crowd, but the food and music is great plus the decor is wild. Nick's a more mainstream but has one of the best chefs in the USA and it's a VERY popular place. Another good place for breakfast is Olga's Cup and Saucer on Point St. They make their own breads as well.
Lupos is the music venue. Public Image Ltd are playing there this Sunday (I'm thinking of going) but there's other places too. Flobots are there on the 22nd and they are a good show.
Lupo's Heartbreak Hotel - Providence, RI If you're here for about a week, then a trip down to Newport is well worth it. Tons to do there too. Google a bit.