Well, what you really want is a the starship Enterprise...
Obviously a nuclear powered submarine would be impossible even for Paul Allen money.
But even if Elon Musk designed a submarine, a submarine is simply too complex of a marine system to realistically manage (outside of the short-duration tethered submersibles used for finding wrecks).
A sub-surface habitat is an interesting idea, but I think the systems involved with air production and circulation would be too complex and the entire thing would be too dependent on energy.
A surface vessel has the advantages of access to wind and solar and it's not hard to imagine a system of fold-out solar panels and fold-up wind turbines to keep a large battery array charged for long-endurance anchorages. Diesel power would only be used to move the vessel to avoid serious storms or seek different anchorages.