Having a family with you changes some of my advice. If you have school age children, you would need to be concerned with the school district you would be moving into unless you would choose private school (unlikely scenario because if that were the case you probably wouldn't be concerned about how expensive NY is).
With kids, your best bet would be either Long Island or Westchester. You would need to do some research into the school districts because outside of NYC each is distinct. For example, my district spends approximately $18,000 per year per student while some neighboring districts might spend only $12,000. But the difference will lie in real estate taxes and assessments and since the average house price in my town is $1.1 million while the county average is about $550,000 my district has a larger pool of money to spend on students. If you are renting rather than buying at first, you should take advantage of the owner's taxes and get the best school district you can for the kids.
Most towns on Long Island and Westchester have parking lots for their respective train stations. Some provide monthly/yearly passes and others may just be meters on a daily basis. Most of the railroad lots are safe and convenient.
One more thing about Long Island though. The traffic generally rivals Los Angeles for being constantly jammed up so that is another consideration if you are looking to drive back and forth to Manhattan.
Brooklyn has some nice neighborhoods and some not so nice ones. You get what you pay for and some of the better areas convenient to Manhattan have rental costs comparable to Manhattan, such as in Brooklyn Heights and Carroll Gardens. Once again, it depends upon whether you have school age children and want to put them in NYC public schools which generally are not known as being as good as suburban public schools.
It seems like you need to get some research done depending upon your family makeup. With kids, make sure the schools are good and worry about the traffic and parking later.
Bob