Check a local map, because maps often have campgrounds listed on them, and you can also look online at the federal site Recreation.gov, which is a site dedicated to federal parks, forests, lakes and museums. The site also allows you to book camping reservations and schedule various activities at the campgrounds.
Another option is to visit a local RV dealership, because people there are likely familiar with camping areas in the area, including some that may be lesser known to the general public. Sporting good shops with extensive camping sections are another potential source of information. If you get to a campground, talk to campers there about other local spots that they can recommend to you.
If there is a lake nearby, drive towards it, because there are often campgrounds available near large bodies of water. Check your phone book as well if you have one, because campgrounds and their booking offices are usually listed. Call a local travel agent to inquire about campgrounds that you can get to, and ask if there are any special activities or deals that are available to you through the travel agent.
Visit a state-licensing office to further inquire about campgrounds in your state. Offices that issue hunting and fishing licenses should be well-educated about all the available camping areas available to you that are close to where you live.