The Lake Tahoe area is actually made up of dozens of state and county parks and National Forest areas as well as traditional parks with playgrounds and access to nature. If you want more of the adult playground with hiking, rock climbing, kayaking and swimming, visit parks like D.L. Bliss State Park on the West Shore or Kings Beach or Lake Tahoe Nevada State Park on the East Shore. Each of these parks offer camping, great beaches, summer events and some really great cliff jumping rocks. Don't forget the incredible Emerald Bay which has camping, boating and exploring in a compact (but stunning) space.
If you have small children, Commons Beach and Kings Beach both have playground and picnic facilities as well as bathrooms and quick access to Tahoe City and Kings Beach with restaurants and hotels. The Taylor Creek Visitor Center is also great for children and the disabled. The paved walking paths meander through creek and meadow areas that are popular with the area's bears.
Even if you want to get away from it all, the Tahoe National Forest and Desolation Wilderness are not technically parks, but they do have designated parking areas and hiking and backcountry ski trails. Many of them also have backpacking areas where you can pitch a tent in the summertime.