Hello Everyone,
I would appreciate your advice/suggestions on following.
I am looking to go out for a day trip with family(with 3 yr kid). Ideal options being: beach swimming, theme park (may be water). I would like to be within NY state but preferably within allegany/central region. Any ideas on locations?
As always, I am getting and is expecting good suggestions through these discussions.

Jones Beach in early Sept. is awesome.

Where are you coming from?

New York is a big state - and there are lots of places you can't do for a day trip unless you feel like driving 10 hours or more.

By Alleghany/Central do you mean Finger Lakes, Olean, somewhere in between?

The Alleghany and Central regions cover a lot of ground. But for what you're looking for, can I suggest either Stony Brook State Park or Letchworth State Park (they are within 20 miles of each other) combined with a trip to nearby Six Flags Darien Lake? Stony Brook is a park built around a small and steep river. You can hike up the river bed and play in several waterfalls and natural waterslides. Letchworth is a giant park built around the Genesee River. It is called the "Grand Canyon of the East," and while it is not going to make anyone forget about the one in the West, it is still pretty impressive. There are three large waterfalls, numerous hiking trails, a restaurant, swimming pools (although I don't know if they'll be open after Labor Day), as well as rafting and ballooning. I've never been to Darien Lake (I hate theme parks), but people love it. Note that Six Flags is seeking to sell/close Darien Lake so I don't know if it will still be open after Labor Day.

rbrazil has the perfect answer!

Thanks all, for gr8 info. rbrazil gave a very good idea. I am coming from/near olean and don't want to drive too far (max 2-3 hrs). I am thinking on Stony Brook State Park or Letchworth State Park. How about waterfalls in sept? will it be too cold?
About Darien six flags, I am not sure, its worth for a 3 yr old kid, tickets are costly...
One of friend suggested a fall season to go to letchworth for beatiful colors.
Any comment?

Most or all amusement parks are closed after Labor Day weekend. Sea Breeze is a smaller scale park for younger children in Rochester with some water rides. There is the Fair Haven Beach (NYS Park). You would have the same problem after Labor Day I would think. Most NYS parks are open until mid-October for camping, but the beaches are closed after Labor Day. Some of the parks have cabins you can rent. There is Water Safari in Old Forge which has an amusement park for the younger children and also a scaled down water park for the little ones. It is just inside the Adirondack Park not far from Utica north on Route 28. Just outside Old Forge (2miles) is Nick's Lake (NYS Park). One mile before Nick's Lake is McCaully Mtn and they usually have chair lifts going up the mtn for siteseers. I'm not sure if Old Forge drive is too far you. These are just suggestions.

FYI: Here is a website for Rochester area for families with children: rochester.kidsoutandabout.com/city-articles/topplaces.html
rochester.kidsoutandabout.com/places/placestogo.html; Sea Breeze does have its own website and is open only the following weekend after Labor Day. You have Lake Ontario right there with a few state parks and lighthouses as well. There is the NYS Fair in Syracuse, NY this week ending Labor Day and many things to do in the area. Green Lakes State Park (although no waterfalls) beaching and camping, the Most Museum (IMAX theater),etc. And the other good suggestions Stony Brook State Park or Letchworth State Park. There is lots to do in this area if researched. Hope this helps.

Hi CherB,
Thanks a lot for all the great ideas.I will do some search on the links provided. That should help me to plan the remaining weekends.
Thanks again...