If you enjoy rich cultural diversity and don't mind the occasional instance of loud music and dirt bikes zooming by in the summer, Elmwood is a fabulous option. It's a predominantly Dominican working class neighborhood with significant Black, Southeast Asian, and White professional presence. It's bookended by Broad and Elmwood, which are busy, lively, and noisy thoroughfares. If you prefer a quieter setting, look west of Cranston Street in the Armory District. Still urban, still diverse, but much more gentrified and expensive. All have great access to a not so great public transit system. Providence is a very safe, walkable city, with the usual property crime (don't leave your car unlocked or valuables on the front seat) that you can expect in a city that continues to grapple with persistent poverty.