I live in the Huntington area. Oheka is beautiful, but they will need a car to go do things. Another poster posted links for things, so I'll give you a little info on them.
The Paramont is a great place to see a show, but beware that most of the tickets are general admission on the floor, no seats. Some shows will have seats on the floor, but no too often. There are seats above the floor though. I think it holds about 1500 people. It's been open a few years now, drinks are very pricey.
John Engeman theatre is fantastic for plays. A few times a year they have people who perform on Broadway come and sing tunes from shows they've been in. It's also a great place for seniors who love to see Broadway plays, but can't really navigate the city. It's in Northport Village, which is a nice small village. They have a nice park right on the water, grab a bench and enjoy looking at the boats. Summer concerts in the park too.
Hecksher Park in Huntington is a town park, so don't confuse it with the state park. The museum has a very good collection of art work, as well as featuring special exhibits. There is a free summer concert series, great music, sometimes dance performances, puppet/children's shows. Worth looking up to see what"s happening at the park. Cinema Arts center is cash only. Caumsett (sp?) State Park is a wonderful place to hike and wander around.
Sagamore Hill, Teddy Roosevelt's home is in Oyster Bay. Very interesting place.
Vanderbilt Museum and Planetarium is in Centerport. Great example of Gold Coast living.
The Whaling Museum is in Cold Spring Harbor. It's a tiny little village, not much going on there, but it's pretty. They could also check out the Fish Hatchery, which is exactly that, a fish hatchery, but it's interesting.
If they want to go to the city they could catch a train from either Cold Spring Harbor or Huntington.
If you have other question just ask, I'd be happy to try and help.