Highland Park was a nice place to be. Walkable, with all the basics right there in town (grocery, pharmacy, take-out, etc.), a mix of grad students, families, some faculty, etc. It is quiet (which can be good or bad depending upon your preference). There are a few small restaurants but not much of a bar or nightlife scene. The walk across the bridge to College Ave or the train station can feel long and cold in mid-winter, but really it's not that bad. There are a few pre-war apartment buildings and a lot of apartments or rooms in old houses. Johnson Park is a great place to walk/jog.
In New Brunswick, the area of George Street between the train station and New Street (and all streets within a couple blocks of that) is the main downtown area. That area is kind of a mix of professionals, some grad students, and I know a couple of professors who live there. There's a small theater district and a few mid-to--upscale bars and restaurants. Rutgers' arts school and the urban planning school are downtown. The train station is right there. Housing stock is mostly higher-end apartment buildings, which can be tough on a grad student budget.
The area along Easton Ave and side streets around it is VERY undergraddy. Frat houses, dive bars, etc. Easy walking distance to College Ave campus and the train station.
Back on the other side of downtown, if you go down George Street a block or two past Morris Street it's pretty sketchy until you get to Douglass campus.
Going down French St or Livingston Av away from downtown, it's primarily working class families from Oaxaca region of Mexico or Central America. Good, cheap food, but not many students live there.
Over in Piscataway, there's not much of a student residential community other than a few apartment complexes along Cedar Lane close to Livingston campus. Otherwise, Busch/Livingston are surrounded by suburban neighborhoods and an industrial park. There are some grad student dorms on Livingston.
Here's a map of the Rutgers-New Brunswick campuses:
https://maps.rutgers.edu/#/?lat=40.5...r=true&zoom=13