for clarification, downtown consists of many neighborhoods: Hamilton Park, Harsimus Cove, Paulus Hook, the Village, Powerhouse, and Van Vorst Park (plus a few more fringe blocks). Also Newport is considered part of Downtown.

Your best bet will be to look at sites like Zillow, or using a local agent like Del Forno or Howard Hanna. In NJ, unlike other places, realtors also work as renting agents. You will need to browse listings, don't rely on them to do it for you, but their websites will be useful. Everything you are mentioning (from Newport proper to Revetment House, which by the way is owned by Newport) are major corporate landlords and the prices are going to be reflective of this.

Also fyi renting is a landlord's market right now. There are literally bidding wars over apartments, with people offering more than advertised to be selected as the tenant. At least that was the case earlier in 2022, maybe it has changed. Ask a realtor about the status on that. Certainly putting in an application on a unit does not mean you will be the "winning" tenant.