I've always thought deep underwater would make sense, provided the containment was very good. You would never have to worry about a meltdown really since there's an unlimited heat sink readily available and the reactor could be constructed to passively cool itself through convection in a total failure / walk away scenario.
Problem is that if you break containment water will carry all that nasty radioactive material everywhere. I'd look at ceramic fuel packaging such as pebble beds or sealed fuel rods that are highly water insoluble, then waste vitrification or encasement in highly water insoluble glass or ceramic materials.
We know how to build nuclear submarines and run them quite well, and salt water is not worse than hot nuclear fuel. Nuclear power will never be easy on the materials side.
Nuclear submarines work well, but they're far from cheap (roughly 5 billion each). lots of that is for stealth and weapons, but it's rather naive to think that underwater nuclear reactors will ever be cost competitive with solar/wind + a battery.
They definitely turn a profit when your country is not attacked and destroyed by invaders, like it currently happens to Ukraine, a country without nuclear submarines.
Well, you could put the containment completely underground, but you'd need to run your coolant of choice up to the surface (and you'd need air intakes for humans etc). You wouldn't need to with once-through water cooling using a large body of water, a river, or the ocean, but that's not allowed anymore.
Note that reactor vessels themselves are sometimes at least partially underground in a reinforced concrete pit in the containment.
