there might be thread(s) for this, cant recall
zurich's dolder was one that came up before
other swiss - la reserve geneva, park hotel vitznau

"museum or other cultural" = any regions to exclude ?
any examples or types, particularly for museums ?

outside rome - La Posta Vecchia
northern italy - villa feltrinelli, castiglion del bosco
venice - could combine island with aman (garden)

FS cairo? combine with FS alexandria
india - taj palace, oberoi, aman, raas, alila

if UAE
outside city - al maha, anantara qasr al sarab, zighy bay
inside city - dar al masyaf, one & only, burj al arab

and or amanyangyun pool villa outside shanghai
could combine with amandayan in lijiang
aman summer palace pool is not outdoor

aman kyoto does not mention pool, nemu not near city
in japan there are likely some ryokans that would work