We have the Iowa (BB61) in San Pedro, the Midway in San Diego and the Hornet in San Fransissyco. All well worth visiting and learning from.
San Fransissyco also has the old Pompanito (?) a WWII submarine.
For the Nimitz to end up as a museum, it needs a sponsor.
USS Pampanito is a museum in SF. USS Hornet is across the bay in Alameda. I've visited both. The Liberty ship Jeremiah O'Brien is in the same area as the Pampanito, and across the bay in Richmond is the Victory ship Red Oak Victory (near a facility that produced Victory ships).
The Iowa was moved from Suisun Bay to San Pedro relatively recently, and I think Midway also became a museum relatively recently (compared to the Hornet and Pampanito). I think 3 or 4 Essex class carriers are museums, as are 3 Iowa class battleships. But of the battleships between USS Texas (pre-"standard") and USS North Carolina, none. Of the surviving carriers on which USN aviation was developed, none. Zero pre-dreadnoughts.
I know, 20-20 geekasoid hindsight.
AFAIK, all museum ships have a non-government foundations that operate the museums.