Excuse my soapbox, for a moment. There’s a myth in our suburbanized world that we should want our kids to grow up in a wealthy, white-bread suburb so that they’ll be safe. It’s a myth, because a bored, overly-entitled child isn’t safe at all: he or she is constantly at risk. Put a kid in a diverse community with some kids that don’t have a lot of money, and even some families that hit the skids, and your child will grow up with a much healthier and more realistic view of the world. End of Soap Box.

Recommended Activities with Kids
Bicycle Ride from Stockton to Llama Farm
(Stockton, NJ) Lovely, challenging farmland ride with payoff in the middle: visiting a Llama farm, open on weekends
Bowman's Hill Hike
(New Hope, PA) Steep climb for serious hiker-dude kids only. Or skip hike and park near tower for the view
Fiddler's Creek Preserve
(Titusville, NJ) Easy ravine hike with mysterious architectural ruins at one end. Only 15 minutes away.
Goat Hill Park
(West Amwell, NJ) Easy walk to spectacular views of the Delaware.
Gravity Hill Farm
(Titusville, NJ) A kid-friendly, beautifully-managed farm right near town (and adjoining Baldpate Mountain)
Hacklebarney State Park
(Long Valley, NJ) Varied hiking from paved paths to narrow scrambly trails. Lovely, rocky ravine. Great place to gain experience.
Hartshorne Woods Park
(Highlands, NJ) NJ's mystery spot: a forest and 200 ft ridge right next to Sandy Hook. Highly recommended
Haycock Mountain at Nockamixon State Park
(Haycock, PA) Superb, intense scramble for experienced hiker kids and parents only. Trail is poorly marked.
Mt. Tammany Hike at the Delaware Water Gap
(Blairstown, NJ) Spectacular hike to an amazing view. Steep. Hiker dude kids only: see Notes for Parents about alt hike to water fall
NJ Transit River Line
(Trenton, NJ) Board a train for an excursion to the Camden waterfront: NJ Aquarium and Battleship NJ, and a ferry ride across to Philly
Patriot's Week
(Trenton, NJ) A full week of events. Battle reenactments are fun, with lots of loud noises and smoke. Keep the dog home!
Picking wild berries at local parks
(Titusville, NJ) Pick delicious, wild raspberries and blackberries along the trails, usually in early July.
Pine Grove Hike on Baldpate Mountain
(Titusville, NJ) Fun, mysterious hike for fit, motivated, reasonably experienced kids. Too long for beginners.
Point Mountain Preserve
(Port Murray, NJ) Great for hiker dudes: varied terrain, gorgeous river, corn fields, steep scrambly climb to panoramic views.
Princeton University Art Museum
(Princeton, NJ) Lots of kid-friendly activities, including special self-guided tours for families, and drop-in events on Saturday mornings.
Roebling Museum
(Roebling, NJ) Well conceived small museum in the Company town. Sophisticated 12+ kids unless you find kid-event on calendar
Sayen House & Gardens
( Hamilton, NJ) Charming free botanical gardens and wooded walks
Schooley's Mountain Park
(Long Valley, NJ) Great for hiker dudes, if you park low and climb up. Pack a lunch and explore the views and Electric Brook gorge.
Self-guided Battles Tour
(Trenton, NJ) Kids can learn that history happened in places they pass every day. The guide gives you the tools to "tell the story" vividly.
Six Flags Great Adventure
(Jackson, NJ) A season pass costs less than 2x a single admission, and lets you go whenever you want: focusing on times when there are no lines
Sourlands Preserve
(Hillsborough Twp, NJ) Extensive trail network, all levels. Big boulders are fun, but require mile+ walk plus 300 ft. elevation gain
Stony Brook Trail
(Princeton, NJ) Go in late spring or summer with water shoes and plan to splash
Stony Brook Watershed Reserve & Center
(Pennington, NJ) Lots of kid-focused events, tots to teens
Teetertown Preserve
(Glen Gardiner, NJ) One of the nicest, closest places to take your kids camping. Little used except when the Boy Scouts show up
Thomas F. Breden Preserve
(Holland Twp, NJ) Little used preseve with nice views of Delaware. Combine it with lunch in Frenchtown or Lambertville for a full day excursion
Trenton Circus Squad
(Trenton, NJ) Kids learn circus skills along with teamwork, discipline, and hard work.
Trenton to the Jersey Shore
(Spring Lake, NJ) What kid doesn't love the beach? Because of I-195, Trentonians miss almost all the traffic
Tyler State Park
(Newtown, PA) Lots of family activites here, e.g. Frisbee golf, horseback riding, canoes.
Valley Forge National Park
(King of Prussia, PA) Lovely hike, with lots of interesting variations, and serious history you can explore in bits. Only 45 minutes away.
Washington's Crossing State Park
(Titusville, NJ) Lovely beginner hikes, only 15 min away, and history too. Check websites (PA as well as NJ) for special events
Witherspoon Woods and Mountain Lakes Preserve
(Princeton, NJ) In Princeton. Charming trails and mysterious boulder formations including the "Devil's Den", which is close to trail head
Woodfield Reservation
(Princeton, NJ) Compact trails to some cool boulders. Can get muddy in spots, and little used (wear long pants, even in summer)
Woods Edge Wools Farm
(Stockton, NJ) The llamas are cute and the farm is very kid-oriented. Bring lots of quarters for chow

A Highly Opinionate Guide to Worthwhile Places