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I forgot to mention the Jersey Journal is a local paper that used to have many apartments listed. I think many were w/o a broker and there were also rooms for rent listed.
Rent.com has buildings and complexes, but craigslist north jersey has houses. They both have their advantages and disadvantages.
Onto places:
Try Bloomfield, on the Montclair side. You can find nice 1 br apts 800-1000 there. The residential areas are nice, but stay towards Montclair and within walking distance of Glenridge station or Bloomfield station. Watsessing station and over towards Newark will put you in an increasingly bad area. Parking can be tricky in this town, too.
If you are thinking of Hoboken, but can't afford it, try Montclair. 1 brs are 1000-1200. The residential areas are very quiet. You are more likely to find a house apartment there, and it has an upper middle class feel -- very large houses, gas lamp posts instead of street lights, heh. It also has dingier areas, though.
NYC train commute from both place is 36-45 minutes. There's the DeCamp bus line, but people complain about it. Buses in general have their issues when it comes to tunnel traffic.
Lyndhurst, Rutherford, and Clifton have 30 minute commutes by train. Lyndhurst is a little overwhelming -- the houses are suburban enough, but the main street is very busy. Rutherford and Clifton have a slower feel and are close to Rt 3 so you still have access to chains and restaurants. Rutherford seems very affluent. You'll run 900-1400 in these places for a 1br.
I would recommend against Jersey City. I used to live by Journal Square, and I never went out at night. Up by Pavonia/Newport and the financial area, you'll find cleaner places, but they'll be extremely expensive.
Hoboken is alright. If you look on craigslist, you can find 1000-1300 1br.
You can also find 1000-1300 1brs north of NYC in New Rochelle and along the Hudson via Metro North. They're a lot harder to find, but they're there on craigslist, and you'd potentially get into Grand Central station in New York in less than 45 minutes. I forget the cut off town for the 45 minute commute.