Lake Miyagase, a man-made lake located in Kanagawa Prefecture, is one of the reservoirs serving Tokyo and Yokohama. Nestled in the Tanzawa mountain range it's a short drive from Tokyo via the Chuo Expressway (exit at Sagamikohigashi).
On the west side of the lake (on Route 64) there is a visitor's center. This center has several restaurants and souvenir shops and parking is 300 yen for the day. If you eat at one of the restaurants check to see if they have parking coupons available. Some do, making your parking free.
In the visitors' center you can get a map of the area (Japanese only) and they also have maps of the various hiking trails around the lake. They had a large map on the wall showing the various bear sightings that have occurred this summer. If you plan to hike make sure you're well prepared and have the proper equipment and a bear bell to make noise to, hopefully, scare away the bears. These may be low elevations mounts (around 750 meters), but they are still mountains, densely forested, and trails can be treacherous even on the lower mountains.
The lake is behind the shops. Walk down the 120 steps to the large open grassy area. This is a good place for the kids to run around, play frisbee, or fly kites. Dogs are welcome, but they have to be kept on a leash and they're not allowed into the grassy park area.
From the steps you'll have a great view of the 315 meter long pedestrian only suspension bridge. From the play area walk along the small river where you can even wade in the cool waters. Small kids seem to have a great time playing in the crystal clear water. Following the path you'll come to a canoe (kayaks, actually) rental center, but it was closed the day we were there. On the other side of the stream there is a BBQ area where you can rent all the equipment and they even supply the food if you want to have a family picnic.
Walk along the short boardwalk over the small marsh area where you'll see ducks. Follow the road around to the other side of the lake, up the ramp, and onto the suspension bridge for a walk back to the park. Along the way you will likely see the boat that cruises the lake. Take a cruise if you want or ride the min-train (no track, rubber wheels) that goes around the complex.
After your walk around the area head back up the steps and enjoy a nice cold cup of kaki-gori (shaved ice) or a refreshing soft cream ice cream cone.
If you go during the Christmas season you can enjoy the Christmas light-up. A 30 meter tall fir tree is festooned with 10,000+ lights and there is a Christmas lights arch. Other trees around the park are also decorated.
By train and bus: Take the Odakyu Line to Hon-Atsugi Station. Then, take a Kanagawa Chuo bus to Lake Miyagase. The bus ride takes approximately one hour.
By car: There are a number of ways to get there, but this is the easiest: Take the Chuo Highway to the Sagamiko Interchange. From there, turn left onto Route 20, then right at Sagamiko Station - make your way to route 412 and head west.
You can find a map (Japanese only) at this site: Lake Miyagase Access Map
I recommend plugging in the phone number for the park into your car navigation system - this should lead you to the visitor center area.