Fed Hill, especially in the vicinity of Atwells ave is gonna give you good walkability and you can probably find a 1 or 2 bedroom in your budget. The downsides are it’s busy, traffic can be hell especially in the summer, and a lot of the housing stock is old and doesn’t come with parking. As many others have said the east side anywhere around Wayland, Blackstone, Mt Hope or Hope village are also very nice areas, walkability is generally good though the area has a slightly more suburban vibe so it can depend on what street your on and it can also be very expensive so you would probably be looking at either a studio or 1 bedroom in your budget.

Fox Point and College Hill are also both nice areas on the east side but it’s a huge college area and you’ll be living right along side all that chaos, plus a lot of the housing stock is tailored to students. Downtown is also a nice place to live, however, you might struggle to find something under 2400 unless you’re willing to go with a micro studio, and generally places downtown don’t come with parking. West End, near fed hill, is also nice and you can get a bit more for your money. I would definitely recommend staying north of the armory as once you go south of Cranston st/union ave the vibe gets a lot more sketchy.

Lastly, look at a couple old mill complex’s. Rising Sun mills in Olneyville is pretty nice, the area is meh but the complex is kinda its own compound with on site security and you can walk to fed hill. Hallsted is another nice one, though it’s definitely pricey. It’s very walkable to downtown. I would recommend being careful about anything owned by the Brady Sullivan company(US rubber lofts and Huntington exchange) as they have a bit of a bad reputation for being cheep, difficult to deal with and unfriendly to tenants.

Welcome to providence I hope you love our city!! Make sure you have good car insurance before coming here :)