Few things:

• Providence used to have an electric trolley system, as did most US cities at the time. Oil and automotive lobbies "fixed" that as the last century went on.
• While related, walkable and transit-oriented are two different things. When most errands and trips out your door can be done on foot - you live in a walkable place.
• RIPTA is fine. You can get downtown in under 20 minutes from most of the city - from there you can shop or run your errands downtown, or transfer to another line and get most places in the state, or hop on the train, or get to the airport. It's not perfect, but it's totally usable for most things.
• If you must use a car, there's Uber, Lyft, Zipcar, etc.
• Bikes exist.

Point is, there are just as many options for getting around here as there are flimsy justifications for car-dependence - it's more of a personal choice and it's largely informed by what neighborhood you live in and your habits/lifestyle.