The Evergreen Lodge is right on the doorstep of Yosemite National Park. A day trip to the valley floor is about an hour away (without traffic). No reservations needed to access the park this summer, but it can get VERY busy during the summer time! Please check the NPS website for more info and consider visiting in the early morning or late afternoon.
Hetch Hetchy is also within the boundaries of Yosemite National Park, but a much closer drive than the valley floor, about 20 minutes up the road. You will still need to pay the entrance fee to the park but usually don't need a reservation. You can walk onto the dam or hike to Wapama Falls (about 6 miles round trip).
This is San Francisco's Family Camp. We have been here as a family numerous times. It is less than a mile down the road from Evergreen Lodge. Easy walk or bike ride. You can purchase a day pass to use their pool, swim lagoon and beach, etc. Fun day trip if you are bringing the kids.
Another option for hiking is Carlon Falls - you will pass by the trailhead on your way to Evergreen. An out and back hike about 3 miles, which ends at Carlon Falls - swimming optional! The trail enters part of Yosemite, but starts/ends on National Forest land.