I moved to Lynbrook a few months ago and have not looked back.
Schools - can't comment, don't have any children in the school system. SD20 seems to be desirable for renters/buyers.
Groceries - Check out Cross Island Fruits. Their stuff is fresher and more affordable than the other supermarkets in the area. There's also an Entenmann's Outlet in the shopping plaza at the intersection of Sunrise Highway and Peninsula. I buy my breads, bagels, and muffins there, some days they're discounted to as little as 50 cents per package.
Food scene - I don't go out to eat much, but I do have plenty of flyers and menus in the mail. Seems like there are many options. I have tried Angelina's for pizza in the downtown area, and also had Cuzco Peruvian Chicken (next to the Lynbrook movie theater). Their food and sangria is pretty good. As someone else said, plenty of options in Rockville Centre, only a few mins drive away.
Mass transit - I take the N4 bus from Merrick Rd and it goes straight to Jamaica Ave for the MTA E, J, Z trains in 35-45 mins. If you end up near the LIRR station, I believe it's a 20 min ride to Jamaica station and 35 min ride to Penn.
The Greis Park recreation center offers Zumba classes to Lynbrook residents at $3 per class, which is a pretty nice deal. The outdoor pool membership is also discounted for Lynbrook residents.
I hope you find what you're looking for in Lynbrook. If you have any other questions, please feel free to ask