Your budget, combined with a fairly modest requirement of 3 bedrooms and 2 baths, opens you up to most areas in central and northern NJ. The only wrinkle: "My commute can't be that long". Monroe Twp is a terribly long commute to NY City. The bus ride by itself is 70-80 minutes. Add 10-15 minutes to get to the bus, 10-20 minutes subway, and 10 minute walk to your building and you are talking a solid 2 hour involvement each way.
Driving might cut that down to 90 minutes. Then there's gas, tools, parking and killing a car every 4 years. But that's too far in my book if you have a family. Underestimating what a long daily commute does to your health and psyche is one of the most common buyers mistakes I see all the time. 3-4 hours of daily evaporated time is bad enough, but the energy output involved leaves nothing for the wife and kids.
Other than that, Monroe is a nice enough. But if it were my choice, I would not commute from that distance. Since a private school is on the menu anyway, move really close to New York to save the wear and tear. Southeastern Bergen County or Western Hudson County might be some places to consider. Very close to the city, and if you leave early, you can drive into midtown in 45 minutes. You can find 3BR and 2 baths for $500,000 quite easily. Think Secaucus, Ridgefield Park, Teaneck, Hasbrouck Heights, Lyndhurst, Wood-Ridge, Fair Lawn, Saddle Brook, Little Ferry.
If you want a sample of some listings from those areas contact me via e-mail.
Member, Worldwide ERC
Licensed Realtor NJ
Licensed Appraiser NJ & NY
Century 21 Joe Tekula Realtors
Agent of the Year 2008
Owner: Sands Appraisal Service, Inc.
Phone (direct): (973) 584-4235