All four nuclear cargo ships have been decomissioned or converted to diesel.
The Russians still have a couple atomic ice breakers that can carry some cargo. Those babies will run you a pretty penny.
Basically I'm looking for a large enough ship that there's lots of room for exploring but not so complicated that I have a labrynith at sea.
If they won't think to go in the ballast tanks, that will work. If they go in them, forget it, it's a pitch dark labyrinth. Also, most cargo ships have rather simple layouts. It doesn't get any sort of complicated until you get into the crew/engine area, and even then the layout makes sense.
Or copied by <Evil Guys> to be used as a base of operations.
I doubt anyone would flag a nuclear ship, and most port states would go apes*** if an atomic plant showed up.
That's not going to work out well unless they stay outside of Everyone's EEZs, and then they'll turn up on the satellite and be investigated. Plus getting decent crewmen to man her, bloody expensive.