Bern
Gurten Park

Join local families, and head to Gurten Park. Take No. 9 tram to the Gurtenbahn stop, then ride the zippy red funicular (Gurtenbahn) to the top of hill.

Make a beeline for the Spielplatz, a fabulous playground with miniature train, big wooden climbing structure, kiddie cars, a Rube Goldberg thing with balls, gears, to push and pull, musical chimes to bong, little pond and rope pulled miniature raft.
Well-marked hiking trails go around the park, and there are spectacular views of the Bernese Alps. Instead of riding the funicular down, follow the trail (route 4) that goes down the east side, ending up at the Gurtenbahn station, takes about an hour.
Tip: Pick up the free map at the Gurtenbahn, with info about 6 different trails.
The park has plenty of grass to run around, shade trees, so bring a picnic (there's also a self-service restaurant and snack bar).
In winter, rent sleds and go tobogganing, fun for everyone in the family.