Take the night tour. Book from
www.alcatrazcruises.com
Combine this into one but food at Fishermans Wharf is the pits. Better food elsewhere. Go there ssrr is best. Don't buy souvenirs from there. Better from Walgreens. Usually cheaper.
Very near to each other. If you are strong, fit and the kids are not with you, you can walk Chinatown and Union Sq in one day. Heck I walk from Pier 33 (Embarcadero) to Union Sq.
Unless you are arty farty, give this place a miss but if you are, great treat.
Just a small street. Take the Cable Car Powell/Hyde Line up to the top and then walk down to the bottom and then take Cable Car Powell/Mason Line back to Union Sq or continue to the end and shop at the Cost Plus World Market.
This one the options to see it are plenty. You can walk on the Golden Gate Bridge. But the best vantage point is on the other side. If you drive the road is usually opened. The time I went the road was closed!

This is Hendrik Point.Else there is an overlook called Vista Point. View is not very good.
Else there is the Marine Dr where you can get access to Fort Point. Yes, you can walk to where Fort Point is but after 5pm they will close the gate to Fort Point.
Didn't go to the Legion of Honor but Napa can be boring. Check out the restaurants at Yountville. I went to Bottega but the one next door is even more satki and kilat! Forgot the name but Yountville is nothing but restaurants!
In short, since Napa Valley is up north and you will have to take the Golden Gate Bridge to go over. Combine this excursion but you may have to leave Legion of Honor out. Rent a car just for a day and return it the same night or next day. As for the photo opportunities, sun rise or sun set is up to you. Sun rise for GG will be foggy. Sunset will be nice with the lights.
No time for Yosemite. Better skip.
Hoover dam is not nice to visit actually. Security is very tight but if you want a great view of the dam, see it at night. Yes, see it at night. If your camera can take it, the view of the dam looks very scifi at night.
South Rim is very far from Vegas. If you are going in summer I recommend North Rim but that will mean you have to book accommodations out of Vegas. Either Kanab or Mt Carmel. The drive from Kanab which is the nearest to the North Rim will take 2.5hrs. North rim will close in Oct onwards.
Horseshoe Bend can be reached easier than the North Rim provided you stay in Kanab. If you stay in Page, even better. As my other thread has revealed, the morning with its rising sun is best to take the pictures of this river feature.
Antelope Canyon is freaking expensive. It is on Indian land. It is holy to them and you pay very high price to just go there and max out your camera's abilities. Good place to stay is Page, AZ to be there. Tours are very limited as well.
Why not take multi-city flight?
What airline you intend to take? ANA allows me to book multicity and I think United as well.
Land SF. You can fly to LV using a domestic flight. Rather cheap. I flew with Southwest but a great experience can be gotten with Virgin America.
Then from LV, fly to LA. Then finally using the original carrier you have flown in to SF to fly back to SG from LA.
Leave the hard touring of UT and AZ. I think easier to drive and not so boring with the scenery.