SMS Goeben (Turkish Yavuz).
Is there really any other? The only WW1-era battlecruiser (or early dreadnought for that matter) still in service in the 1960's with few modifications. The ideal solution would be for her to be sold back to Germany and refitted as she was in 1914 as a proud member of the (politically not too sensitive) High Seas Fleet Mediterranean squadron whose transferral to Turkey expanded WW1. With this history, she could serve not only as a naval musem, but a museum dedicated to the entire First World War. Too bad the Turks scrapped her.
The problem with most other WW1-era ships like Dreadnought is that they were not considered "historic" when obsolete. Also, the Washington Treaty required most obsolete ships to be scrapped, not just deactivated. As noted, "Warspite" or one of the "R"s could conceivably been retained, but in 1946-48 people wanted scrap value for all that steel, not museums.
Other WW1 era ships that could conceivably have been saved were the South American dreadnoughts. Still in service in the 1950's and quite old. However, I suspect neither Argentina, Chile, or Brazil saw them as particularly historic or worth preserving, and its hard to imagine enough interest in Britain or the US to buy and preserve ships that did not serve in their own navies. A Chilean ship maybe, since they also were purloined by Britain in WW1.
The only other likely candidates would be a few British and French battleships or heavy gun crusiers that served into the late 1950's or 1960's. One of the Richelieus would probably be the most likely candidate.
An Italian Cavour-class ship is also a remote possibility, and several Russian dreadnoughts survived in the USSR long after they lost all miltary value.
It's no suprise that almost all large surviving museum ships are American. The US had the money to keep their WW2 battleships in service or inactve reserve far longer than anyone else, so they weren't scrapped. In fact, most 3rd generation US battleships escaped the breakers, and even one old WW1-vintage ship as well.