So much to do, so much to see.
Hi Simon, and Welcome to the Great American roadtrip Forum.
Since you are staying in Williams for your visit to the Grand Canyon, I would urge you to try and manage to experience a sunrise or sunset over the canyon. It is an unforgettable experience, and definitely worth the drive in the dark either to get there, or get back.
I assume you know that London Bridge is in Havasu City.... a nostalgic touch of home for you.
You could also experience the best section of Rte 66 from Seligman (exit 139 off I-40) to Topock (Where the Mother Road meets the Colorado). This would take you through Kingman and the quaint little town of Oatman (where burrows roam the main street). Spectacular country as you go over Sitgreaves Pass. A genuine Rte 66 experience, especially in a Mustang. From Kingman to Topock it's as if you are driving in the 50's. That would be fantastic in a car (almost) from the era.
Lifey
Another Possibility (Of the Several)
As the other responders have pointed out, two days is more than enough time to get from Williams to San Diego and there are several possibilities for a route. But if you've hired a road car and are looking for a RoadTrip, then you might as well avoid the motorways and stick to the roads. Donna's suggestion of AZ-89A south from Flagstaff through Oak Creek Canyon to Sedona is an excellent place to start. From there continue on AZ-89A through Cottonwood, past Tuzigoot National Monument, through Jerome, and on to Prescott. At that point it will be time for some open road through the desert: AZ-99 and AZ-71 to Aguila and US-60 west. After a short bit on I-10, AZ-95 will take you south to Yuma. From there, there's another unavoidable stretch of motorway, I-8 to into the Imperial Valley (below sea level), to get to CA-98 through Calexico, and one last bit of motorway (I-8 again) to CA-94, a very scenic road through some low mountains, which will take you the rest of the way into San Diego.
Quartzite AZ would be the roughly halfway point and although it does cater more to the RV crowd, you should be able to find some decent lodging there. My wife and I have enjoyed Silly Al's Pizza when we've stopped to eat in Quartzite.
AZBuck