If you open Google maps then plot the Tower Museum there is a button at the top (on a laptop) you can press to show you parking.
Three car parks show up within a 3 minute walking radius- Quayside, Victoria Market and one on Foyle Street [this latter apparently closed to end of next year] just behind the Bus Station. Click on each car park and it shows you the walking route to the Museum.
Then this is the Derry City Council page about car parks- location, size and what they charge- https://www.derrystrabane.com/services/car-parking-information/derry-city-area-car-parks
Quayside appears to be part of a shopping mall.
Someone on another very recent thread wrote that parking in Derry is difficult, and suggested arriving by bus or train.