Providence downtown is nice area for walking around if the weather is nice. Check the schedule for Water Fire ( http://waterfire.org/
), it's always nice esspecially if it is a dance night. Brown University area is also nice for walking, you generally do not need the car around downtown. There is plenty of great places to eat, starting from the front of the Providence Mall, few great bars right accross the mall, Trinity brew house of you are fool for fresh brew beers (you see the process/equipment through the glass wall sitting at the bar), few really good restaurants ($$ to $$$), if you are OK with more pedestrian food then checkout Fellini's pizzeria (open until what, 4AM usually, BYOB is OK) and Coffee Exchange coffee house on Wickenden street ( http://sustainablecoffee.com/about-us/our-mission.html
); also some good Asian/Indian food there, and Wickenden pub (known as Wick with locals
). Wick is bring your own food place, their specialty is beer
I wouldn't hang out much in the mall really if the weather is nice; downtown simply has too much to offer.