My husband suggested that I respond to you, as I was born and raised on Long Island and then moved to Indianapolis when I was 21 and lived there for 5 years. So, I have experience with both areas.
The people and lifestyle is very different from one area to the other, therefore you really need to decide what factors are most important to you. The cost of living is extremly high, not just the housing prices, but the property taxes as well. My parents property taxes were only about $5000 when they first had their home built and today are hovering at $30,000. However, they purchased their home for $150,000 and today, 28 years later, the home is worth about $1,800,000. A pretty good investment.
Most of your taxes go towards the school system. The schools are highly rated and have extremly high graduation rates and excellent music/arts programs. The extracuricular activities are also wonderful. In the right area, there is very little in the way of gangs, and bad kids, but drugs do exist. Mostly to the very rich kids, because they have nothing else to do with their money. Clothes, cars and material possessions are very important to students/families and if you don't have the money to keep your children in style, you may want to rethink the move, because they will be outcasts.
There is much to do on a daily basis. Lots of cultural events and things to keep children busy, therefore keeping them out of trouble. Teen pregnancy and drop outs are of very little concern and your children with most definitely get to go to a fantastic college with the education they are getting.
People are not nearly as snobby as they are made out to be once you get to know them. It is a different general attitude and once you get used to it, it really won't bother you at all. My mother grew up on a farm in Indiana and moved to L.I. when she met my father at Purdue and she loves it there. She would never move back to Indiana. On the other hand, my husband who was raised in Indianapolis, would never consider moving to L.I. He hates the traffic, and density of people.
The statement made in a previous post regarding the South shore vs. the north was extremly inaccurate. The North shore is a beautiful area and just because it is more expensive to live there, doesn't mean that people are snobby. There is a rivalry between the North and South shore that has existed as long as I can remember. The people from the North Shore saying the people from the South are low class and the people from the South saying the North is snobby. The real facts are as follows: It is the same as people from Carmel saying that people from Greenwood live in a crummy area and are low class. They are 2 different areas of income and therefore are going to be perceived differently.
As for myself, I have always loved L.I. and wouldn't mind returning, but it isn't for everyone.
I am more than happy to answer any specific questions that you may have. The more detail you can give as to what you are looking for in your home base, the better answers I can give you. I hope this has helped. Good luck with your decision.