Fed Hill/West End is what it sounds like you want imo. It's close to everything and very walkable. Elmwood tends to be louder, have more cars, and parts of it feel more run-down. The scene there is chill (lots of DR culture), whereas further north it's more Italian (e.g. Atwells is pretty much little italy). Elmhurst area is more like suburbs on the west side, which maybe you want to look into. Same with Silver lake but I haven't explored much down there. People on here like to make a bug deal about the crime in Prov, which admittedly seems worse around Broad st. But it's overblown, the crime rate here is very low, especially compared to what I hear about Hartford.

If you're looking for cons, realistically the thing that Providence has particularly bad is road rage and especially noise pollution. As for pros the food is phenomenal for how small the city is, and there's a couple really walkable neighborhoods. It takes 20 mins before you're in the woods, plus it's a satellite town to Boston so you have easy access to the full spectrum of nature - full city life without having to live in a giant city or out in a cabin.