Parks
Parks can be big or small and in some places may also be referred to as playgrounds if specifically geared towards children.
The United States has a large national park system http://www.nps.gov/findapark/index.htm, and you may want to visit these large parks during your time in the US. If you are lucky enough to live near one, you can take advantage of the hiking, camping, fishing, and other activities more frequently.
The state you live in will most likely have several large State Parks ( https://en.wikipedia.org/wiki/Lists_of_state_parks_by_U.S._state). These are wonderful places to spend the day for hiking, picnicking and enjoying the natural surroundings.
Closer to home, your town or county ( a larger area that has many towns within it), will most likely have town parks and recreation areas. These may include playground, splashgrounds (for summer fun in the water), trails for hiking, walking and bike riding, skate boarding. Your host family will be able to direct you to the “favorite” park for their children. Some families may have a membership at a local park pool in the summer. Be sure to ask! To find a park near your home, google the term “find parks near (add your town or zipcode) or try http://www.discovertheforest.org/?m=1#map
So be sure to enjoy all the beauty and nature you find in a park!