Nazira, if you are staying at the Biltmore hotel you will not ever need a car to hit most of Providence's high points. It is a compact walkable city with a vibrant alternative nightlife, spectacular restaurants, and amazing live music and theater venues. The few things that are probably not walkable can be easily reached by the excellent trolley system. Every time I go back to Providence (nearly every month although I live in Florida) it is more diverse and more dynamic.
I recommend:
the RISD Museum of Fine Art on College Hill.
Gracie's Restaurant downtown or Chez Pascal on the East Side for a 5 star world class meal
Almost anywhere on Wickenden Street/Fox Point for a cheap and excellent ethnic meal: cambodian, vietnamese, japanese, indian, vegan, korean, new american, etc. Plus numerous live music venues.
The Federal Hill area is renowned for its Italian-American restaurants, pastry shops, and public squares. Unpretentious and friendly.
Grab a free copy of the Providence Phoenix, the local alternative newspaper as soon as you arrive so you can get the latest listings for clubs, live music, theater, independent movie nights at Brown University or other things going on. There is something amazing happening almost every night.
Have a wonderful time!
Frederick
fwright@myself.com