Here's a map: https://maps.usgs.gov/padusdataexplorer/#/public-access (edit: this map viewer isn't super clear, but go to the Public Access tab. You can zoom in and click on an area to see who manages it. Google it by name to look up specific rules & regulations). They encourage you to use it to find campsites: https://www.protectedlands.net/uses/pad-us-2-0-helps-rv-user...
There's a lot of different public land classifications, with different rules and administrators: https://www.doi.gov/blog/americas-public-lands-explained
In general, you're most likely to run into free camping on USFS or BLM land, which also tend to be mixed-used (as in not reserved for recreation, but also used for forestry or ranching etc.).
Pretty much every state West of (or split by) the Contintental Divide, not just the Pacific Coast states and some of the adjacent ones.
VA/WV has the George Washington National Forest, Mt Rogers National Recreational Area, Shenandoah National Park, multiple Wilderness areas (Dolly Sods, etc). Abundant state parks with a mix of established campgrounds and backcountry camping.
We don’t have the huge swaths of BLM land. But outdoor access is still pretty great (at least from the DC/Mid-Atlantic urban corridor).
There's a lot of free camping out there, you just have to look for it.
What I call the greater west (all of the “West”, “Southwest”, and “Pacific Northwest”) are largely public, federal lands.