As an American, you can only visit during the Mass games unless they've changed that. I've been thinking about a weekend trip one of these days (but probably October given that's the only time I can go).

They've changed it. You can go at certain periods during the year often coinciding with key events.

And you can only go as part of a set tour which is usually over a week. So no weekend tours and certainly not by yourself.

IIRC, the last person to individually book a tour to North Korea decided to shirk his appointment with the state ministry in charge of chaperones and took advantage of the fact that a Trans-Siberian railway crossing was listed as a valid port of entry on the standard tourist visa... it's not often you get to play with (if only mentally now) the technicalities of international transit. It makes you grin like hell.