“Best” route depends on what you’re looking for in the trip.
The most straightforward route from San Francisco to
Disneyland is I-80 across the Bay Bridge → I-580 → I-5 all the way down the Central Valley straight to Anaheim. That’s an approximately 7-hour trip. Five of those hours will be through hundreds of miles of agricultural land with no really notable sights, just many pit stops.
Since you mentioned an interest in the scenic drive down the coast, you may want to take a combination of CA Hwy 1 and US101. If you plan to make this drive, I’d echo the suggestions that you spread the trip over two days -- or even three days -- to fully enjoy the sights. The drive along the coast -- particularly as you hit Big Sur -- gets very windy. You’ll probably be stopping at a lot at vista points, your driving speed will slow for the many curves, and it’ll take much longer to cover the same distance. But it’s worth it!
If you plan to drive down the coast, there isn’t really a much better time to do it than in May. I did a similar drive with my family last year in mid-May, and it was breathtaking. The rainy season in California usually ends by April, and it was clear skies and high 60s-70s degree weather last May. The hills are still green from the winter rains (they dry out as summer sets in), and they’re usually covered in wild mustard and other wildflowers. In September, much of northern California settles into a kind of Indian summer. Things get hotter and it's usually dry when most other places are getting colder and wetter. The hills are dry and not very scenic.
The route you take really depends on how much time you want to spend driving along the coast. As I mentioned above, the coast is beautiful, but winding, so the longer you spend driving it, the more stops you’re likely to make to sightsee, and the longer your trip will be. For some people, it can also get a bit monotonous, especially away from cities to mark your progress.
So, from SF, you’re heading south, with a goal of hitting Hwy 1. You can actually get on Hwy 1 early on by leaving the SF on I-280, take the Pacifica exit onto Hwy 1. From Pacifica, you’ll begin to see the rugged coastline to your right, passing Half Moon Bay, Pescadero, and eventually hitting Santa Cruz. If you have time, the little towns are worth a visit. At Santa Cruz, there’s the Santa Cruz Beach Boardwalk that might be of interest. If you have more time, the Roaring Camp Railroads runs a train between the beach boardwalk and a patch of redwood forest further up the mountains.
From Santa Cruz, you’ll want to head to Monterey. Monterey is full of touristy things to do, including Cannery Row and the Monterey Bay Aquarium, located at the end of Cannery Row. In May, you’re at the tail end of the Grey whale migration, and you can take a whale watching tour from Monterey if you have the time. Santa Cruz Boardwalk and Cannery Row in Monterey could be a cool to include on your trip to Disneyland since Disney California Adventure pays homage to places like these at Pacific Wharf.
A few miles south of Monterey, you can do a scenic 17-Mile Drive through Peeble Beach. The drive has a small entry fee per car, but it takes you through the famous Pebble Beach golf course and along some beautiful coastline where you can see seals and seabirds up close. During the drive, you’ll also see the iconic cypress tree that’s on the logo of Pebble Beach.
About 10 miles south of Monterey is the small town of Carmel-By-The-Sea. My family loves weekend getaways to Carmel. It developed as an artist community, and you’ll see an abundance of galleries. These days, it’s an upscale retreat with good shopping and restaurants. Carmel Beach is wonderful on a nice day, and curves like a small bay. A little south of Carmel-By-The-Sea is Carmel Valley, which is home to a number of very nice wineries.
If you decide to pack in a lot of activities on this leg of your trip, Monterey or Carmel make for a nice place to spend the night. You can find hotels, inns or B&Bs in a wide price range. Or, you can decide to cut out this part of the coast (since you’ll see a lot of it in Big Sur) and Santa Cruz to make a more direct drive from SF to Monterey (US101 out of SF → Hwy 156 to connect to → Hwy 1).
Once you pass Carmel, you’ll quickly enter the stretch of the coast that is Big Sur. Fill up your gas tank before leaving Monterey or Carmel, because there is maybe one gas station in Big Sur and that station was charging about $6/gallon for regular gas.
Sights worth stopping for in and around Big Sur include Point Lobos, just outside of Carmel; the Bixby Bridge; McWay Falls; Pfeiffer (Purple Sand) Beach; and just about all the vista points. Places to eat in Big Sur are also very limited, but I’d highly recommend Nepenthe (if you don’t mind the usual wait). Good food, but amazing views! This part of the drive can easily take up half your day. As you exit Big Sur, you’ll notice a gradual change in the terrain. The land becomes more rolling hills and the roads are straighter.
About an hour south of Big Sur is the Hearst Castle at San Simeon. Unfortunately, you can’t really visit without purchasing a tour (info on their website). Around San Simeon is the Piedras Blancas Rookery, where hundreds of elephant seals make their home. About 10 minutes south of San Simeon is Cambria, a cute town with good restaurants, shops, a lot of lodging options. In Cambria is also Moonstone Beach, which is worth checking out for the moonstones that usually cover the beach in late spring. Depending on how you plan your trip, Cambria is also a good option to overnight. A lot of the town’s lodging is along Moonstone Beach, which has a nice boardwalk to stroll in the morning or evening and is literally across the street of the motels.
Cambria is kind of a geographic halfway point between SF and LA along the coast. At this point you’ve seen a lot of the coast, so you can decide to head east along CA Hwy 46 and connect with US101 or I-5 heading south to LA and then Anaheim. Hwy 46 is very scenic and takes you past a lot of wineries in the Paso Robles area. Or, you can continue south on Hwy 1 to Morro Bay (already mentioned), then connect with US101 at San Luis Obispo, and onward to Pismo Beach, Santa Maria (Santa Barbara’s wine country around Santa Ynez and Los Olivos is worth visiting if you’re into wine, as is the Danish village of Solvang), Santa Barbara, Ventura … LA … Anaheim.
If you have any questions, post it and I’ll try to check back and answer if I can. I love this trip, and I hope you’ll enjoy yours.
Good luck!
It is a very beautiful road and there are some great things to see along the way - e.g Monterey, Santa Cruz (boardwalk), Big Sur, Julia Pfeiffer Burns State Park, Hearst Castle, Piedras Blancas (elephant seals), Cayucos, Santa Barbara, Santa Monica/Venice Beach and many more!
It should take at least 2 days - but you could also spend an extra night or five before driving to Anaheim 
