The rental market in Princeton is quite mixed - there are some apartment building but most are subsidized housing for lower income levels. There are several older homes converted to two or more units and many single family homes owned as an investment.
The rentals range from $350 to $600 and up, depending on the size and location. Some are lower but hard to find and may not be kept up well. Most landlords I work with do not want pets and require deposits and references. Allow about a month for find a suitable rental.
If you email me I will look over the rental ads in the local newspapers and let you know if I have anything available.
I may also be able to help with a low or no down payment loan where you could own a home for about what the rent would be. Ask me!