I agree with the Los Angeles assessments here. Not only is travel (air or ground) going to consume a day, but LA requires a lot more time to visit. Universal Studios/Universal City walk would consume a day in itself. Another for Hollywood boulevard and vicinity. Disneyland (60-120 minutes south, depending on traffic) is an entirely different can of worms, requiring multiple days and lots of extra cash. And there is a lot more to see than the iceberg tip I've mentioned...
On to SF. I'd recommend staying near fisherman's wharf if you can, or maybe the Hyatt Regency in the Embarcadero. There are fisherman's wharf and the piers in and around pier 39, a Bay cruise starting from the same area, riding the obligatory cable car from there to see Union Square and downtown Market street and back again. Don't forget to visit Chinatown and possibly the lesser-known Japan town. You could walk across, or at least out onto the Golden Gate bridge (if you're up for it) and definitely visit Fort Point underneath the bridge.
There's Coit Tower and that one twisted block of Lombard street (with the 30 to 45 minute multiple-block line of cars waiting to drive it), the Haight-Ashbury district and the head of Golden Gate park near there. Continuing westward through the park from that starting point, there is the large conservatory, then The Academy of Sciences and the De Young museum, across from one another in GG park at around 10th Avenue and the Japanese tea garden in the same area. There are still more places of interest in the park. A tour of Alcatraz would be on my list. Those also originate from the pier area. You might consider a visit to Angel Island but you probably won't have time.. And we haven't left the city yet.
In Marin county, just north of the bridge, there's Sausalito, Tiburon (which you can just view from afar when in Sausalito, lol.) and Muir woods (highly recommended). You can either drive to Sausalito or take a ferry from the aforementioned pier area, which affords another chance to get out on the bay. I think Muir woods requires a car unless there is some tour bus company running out there that I don't know of, which is very possible.
Depending on your willingness to travel, there's the Napa Valley wine country corridor to the north, including St. Helena and Calistoga. The center of the valley is between 50 (80km) to 70 miles (112 km) from SF, depending on which way you go and requires about 2.5 hours travel each way. Since you don't drive, you'd have to find a wine tasting or similar tour but that shouldn't be difficult.
To the south on the coast, Half Moon bay is only about 10 miles (16km) away. Santa Cruise is about 80 miles (130km) and two hours south. Farther south, about 120 miles (195km) from SF, you'll find the Monterey Bay aquarium, Carmel by the Sea and Pebble Beach. Hearst Castle is 250 miles (400km) south and basically half way to LA. Each of these destinations aside from Half Moon Bay would require a full day at least and probably won't make your itinerary but are worth considering.
Vegas. I suggest staying center Strip if you're a first timer. The rest of us get over the strip but it really is something to experience if you've never been here. Don't miss the downtown Fremont Street Experience area and come at night to see at least one or two canopy light shows, which run at the top of each hour in the evenings. If you watch TV and are interested, the Pawn Stars shop is not far from downtown on Las Vegas Blvd and there is a loop shuttle bus that will take you there. To be honest, it's mostly a tourist trap gift shop but there are some of the items from the series on display in glass cases.
You should see the Bellagio conservatory and watch the fountain show out front on the Strip. Definitely book at least one (or two) Cirque Du Soleil shows. Mystere and Love are favorites. Look for discount tickets. You can view the strip from the Linq High Roller or the entire valley from an even greater height by visiting the Stratosphere tower. Tip: They charge to go up to the top but not if you go to the bar or the restaurant and once you're up there, you're up there and free to change floors
. You can also pay for a package that includes some/all of the rides at the top if you like that sort of thing.
You've already mentioned the Grand Canyon and that's a definite must-see, but don't forget Hoover Dam. It's also worth a visit and there are bus tours, but try to arrange an inside tour of the dam if you can. It's worth it. I recommend the longer "hard hat" tour.
Out of town we have nearby Red Rock canyon which is very popular. Mt. Charleston and the Valley of Fire are farther away in different directions and are about an hour northwest and northeast of Vegas respectively. The Valley of fire is more spectacular than Red Rock (with my apologies to Red Rock) but not having a car will make visits to these places difficult.