Possible to camp in seclusion instead of public camping grounds?

[Jack White]

My friend is going to visit me and we want to save money. So, instead of getting a hotel, we want to try camping for a few weeks. We don't really care about the conditions too much, as long as it's safe. The problem is, we don't really want to do a big public camping grounds thing, because she has social anxiety, so we want to be alone and away from people. We don't want to be deep in the woods or anything either though, as we don't have a lot of camping experience.

Anyway, I'm wondering what our options are? Are there any places we could go where we wouldn't have to deal with a lot of people and where we could have privacy? It's illegal to just set up camp anywhere right? This would be in Massachusetts by the way.

Thanks!