There’s only one answer for you, then–Highland Park!
I lived there for 2 years when I was just out of college. It is a great great place to live–it’s a real community with all the amenities, but it is still sort of a college town. You’ll find lots of college and grad students there, and the types of businesses that cater to them. I found that people were really friendly, and it was very easy to make friends.
It’s a short walk to New Brunswick, where you can go to your classes and catch the train. New Brunswick also has a great nightlife. Tons of bars, bands, restaurants, the State Theater, etc. Both Highland Park and New Brunswick are very diverse communities, too. I don’t know what you’re into, but you’ll likely be able to find some like-minded individuals.
There are plenty of apartments to be had in Highland Park. It’s not the cheapest place to live, but it is not especially pricey either.
You could also live in New Brunswick, but some parts of it aren’t so great. It’s worth looking there, too, I suppose.