I am an equestrian, and am intimately familiar with areas that would meet all the criteria as you have outlined. There are several communities with 1 acre zoning that have homes on 1-5 acres. In this segment, you will have many options and choices. You will certainly find several options over 5 acres also.
Monmouth County provides easy access to NYC (particularly Wall Street - since it is the closest via ferry), and everything you could want. I have lived in Southern CA, Greenwich, CT, and now in Rumson, NJ. You can really have it all here. Access to the city for work or play, and an almost endless array of opportunities for recreation and social activities. Red Bank is a nucleus for dining, local theater, arts and many outdoor festivals, including jazz festivals, tree lightings, car shows, etc. Options for water and shore activities are extensive. Multiple waterways are extend from Sandy Hook Bay and off of the Shrewsbury River and Navesink River. The bay attracts windsurfers and kiters. Small boats are a welcome presence in the tributaries, and larger boats find a home in a number of marinas. The park systems are phenomenal with activities for all age groups and extensive networks of trails. Bike lanes exist on many streets and through Sandy Hook for cyclists. Beautiful boardwalks accommodate runners, walkers, strollers, and those who just want to sit and take in the views. Dining options are plentiful. As mentioned earlier, I am an equestrian enthusiast. Riding trails, stables and lessons are plentiful. Some of the top rated restaurants in the state are located in the immediate area. If you want to shop until you drop, you can do that, too.
I have been a Realtor and lived on the shore for 10 years. This is really a place where you can have it all. There is a great sense of community here. Here are a few links that might be helpful.
http://seastreak.com/SeaStreak - Ferry Info from Atlantic Highlands & Highlands
http://www.nywaterway.com/ferry/schedules/ferry-route.asp?fe - Ferry from Belford
http://redbank.com/ - Voted the hippest town in NJ
http://www.monmouthcountyparks.com/parks/hartshorne.asp - Hartshorne Woods
http://www.sandy-hook.com/sandy-hook-map.shtml - Sandy Hook Park - 1600+ Acres
http://www.piervillage.com/ - Boardwalk and Village at Long Branch, NJ
http://mls.momls.com/MonmouthReports/listings.asp?ID=7222471549 5-10 ACRES (some are close to the ferry, some are not...provided info county wide for comparison)
http://mls.momls.com/MonmouthReports/listings.asp?ID=7222471562 2-5 ACRES (narrowed to mostly Northern Monmouth County)
Every school in NJ is rated in the NJ School Report Card
Also, check out
http://GreatSchools.net (Has comments and feedback from parents and students)
http://SchoolMatters.com (By Standard & Poors)
Yes, you can have it all here!
Deborah Madey - Broker
Peninsula Realty Group
Your question about towns in the NY metropolitan area that offer a reasonable commute to Manhattan, open land and great schools either public or private. There are so many all around the metropolitan area. Gail is correct that the Huntington Township area is wonderful.
In what County do you wish to live: Westchester, Bergen Nassau, Suffolk, etc. Bergen County offers some terrific towns to live and fulfill your requirements. Downtown Brooklyn also would offer you a wonderful commute, backyard, great private and public schools. I am NY State licensed Real Estate Broker and know Bergen County very well.
Good luck in your search,
Check out the schools at http://www.GailGladstone.com and click on "school info." It's a great place to live! You can find parcels with good acreage in Ft. Salonga and all around Huntington Township.