Being from Brooklyn myself, Benshonhurst to be exact, and having moved to NJ in 1983, I welcome you, and the idea of moving to the great Garden State.
Depending on your price range, there's many towns that meet your needs.
However, I can highly recomment Metuchen NJ. Not as pricey as some of the other towns mentioned.
It's a small town, with a lovely Main St, and has it's own train station direct to NY. Only 1 high school, 1 middle school and the elementary is split in upper and lower school and the diestirct is well ranked in NJ..
Main St is tree lined, and there's always something community based going on within the town. There's a YMCA, for classes, camp, swimming, exercise etc. It's within minutes to the GSP, Turnpike, Routes 1 and 287, and close to the Menlo Park and Woodbridge Malls.
If you are interested in learning more about this town, and/or asking questions about a few others that were mentioned, feel free to email me directly, or give me a call for a no obligation chat about your needs, and what might suit you best. I look forward to hearing fom you :)
PruMaryNJ@aol.com or 908-675-0167