I agree with those who say to park either in LeeVining or Glass Creek and enjoy the scenic drive. We have a home in Mammoth Lakes and usually make the drive once or twice a year from there. Leaving from ML is a half hour longer than from the Whoa Nelly Deli.
Don't forget that behind Mono Lake is Adobe Valley and the wild horse population of about 250 horses.
North a little is Bodie St Pk. An old mining town that is being kept in what the state calls a state of arrested decay. It hasn't changed much since our fifty something girls thought it was fun to drop rocks in the cow pies to hear the "galoop sound".