Take a spin on the ice at Bayville's Winter Wonderland. Photo by the author.

Bayville Winter Wonderland — Bayville
If you haven't visited Bayville Winter Wonderland, today is your last chance to take advantage of the park's seasonal activities, which include outdoor ice-skating, rock climbing, arcade games, Santa's Toy Factory Funhouse, a train ride on the Bayville Holiday Express, and an opportunity to meet (and thank) Santa for all of the goodies received this year. There's something for children of all ages. 

Bounce it out —​ varies
Kids can shake off that lingering cabin fever before heading back to the classroom at Bounce! Trampoline Sports in Syosset, Air Trampoline Sports in Ronkonkoma, or Bounce U in Oceanside. All three offer New Year's Day open play (read: jumping) sessions, though you may want to reserve your slot ahead of time. The indoor amusement park, Fun Station USA in Lynbrook is open too, if you're looking for bumper cars, video games, and more kid games, and so too are the local Dave and Buster's locations.

Let's Celebrate the New Year — Port Jefferson
It won't be long before your kids are back in the school swing of things. Help them brush up on their math skills at Maritime Explorium, which is hosting an event that allows kids to create their very own New Year's Eve-style Times Square ball using the principles of geometry and design. 

Ice skate —​ varies
Hit the ice for both indoor and outdoor skating. For example, the Port Washington Skating Center continues to offer its Holiday Skating Session today, including an early evening Puck Shoot session for kids looking to test their hockey skills. 

Roller skate – Seaford 
United Skates of America opens at noon on New Year's Day, offering an indoor diversion for all ages.

See the Boardwalk Lights before they come down.

Boardwalk Lights — Long Beach
This holiday nautical themed light show on the Long Beach Boardwalk wraps up in the just a few days—but it's not too late to pack a thermos of hot cocoa, stroll by the sea, and take in holiday light splendor. FREE

Go bowling — varies
Many AMF locations are open like Syosset Lanes, as is The All Star in Riverhead, Coram Country Lanes with its "mini bowling" for tots, and many other local lanes. Check out our list of bowling alleys in Nassau County and in Suffolk County.

Visit the aquarium
Yes, the Long Island Aquarium is open New Year's Day! Although they might be cleaning up from the prior night's New Year's Eve family party, you can still visit with the fish, coral reef, turtles, alligators, and even parrots.

Explore the Cradle of Aviation — Garden City
Play video games at the retro arcade exhibit, explore the Junior Jet Club with tots, go on an alien planet scavenger hunt, or catch a show (One World, One Sky: Big Bird's Adventure is playing) at the planetarium at the Cradle of Aviation Museum, which remains open today. Take a spin on Nunley's Carousel afterward.

Ride the train into NYC
Try the Immersion Room at Cooper Hewitt or the oversize touchscreens, the seasonal Butterfly Conservatory at the American Museum of Natural History, children's theater, or grab lunch and then walk around the city, soaking up the final holiday scenes. There's plenty open in NYC for families on New Year's Day. Prefer a road trip? The 12 days of science fun with liquid nitrogen ice cream, snowflake construction, and more continues at Liberty Science Center just over the border in Jersey City. 

Rock climb — Plainview
Always wanted to try rock climbing? The indoor Island Rock wall is open for climbing fun on New Year's Day. It's the perfect all-ages sport.

Share sushi — Manhasset
After a long week of cooking and feasting, take the day off from the kitchen and enjoy a sushi meal at Benihana in Manhasset or Westbury, where kids can watch (in amazement) as chefs flip and prepare meals mere inches away from your table. 

Stroll along the beach 
Walk along Jones Beach to collect shells, or another local beach, for a peaceful way to ring in the New Year. The Fire Island Lighthouse Preservation Society will also host a morning hike that kicks off from Robert Moses State Park. FREE

Top photo: It's the last chance to go to Bayville's Winter Wonderland before it closes for the season. Unless otherwise noted, photos courtesy of the venues/events.