"Beach cruisers" are pretty much made for riding around flat land. They got associated with beaches, apparently, due to California and Florida being flat, so you find them near beach resorts.
History writers are a funny bunch, and you can find a lot of books with non-facts in them. A lot of experts in a lot of fields can cite a lot of things that never happened or are entirely non-true, but are common knowledge in a field. Everything from engineering to computers to bioscience has this, some "authority" writes something silly down and everyone buys it. Someone, at some point, wrote down in a book about American bicycles that "beach cruisers" were made to ride around on sand at the beach, and it stuck.
Funny enough, balloon bikes (so called due to their wide, low-pressure tires) were the base platform for mountain bikes, which do handle random terrain (and hills) to some degree; so there is a degree of truth to this...
Sorting out the whole story behind bicycle history would be interesting. I don't think it's readily accessible, and you'd have to do some digging, probably through bike companies as well as history books. Bike companies will likely have a lot of records that go, "What? Yeah, that never happened" when you flash "history" texts written by silly romantics past them.
Look for a nice hybrid or road bike, depending on your fancy. Hybrid will probably come stock with some lower gears; mine doesn't go into the mountain range, though, and I want to fix that....