I stayed at the Sheraton Fisherman's Wharf while vacationing a few years ago. Although it's a Sheraton, it's nothing special, but the location was excellent (10 min walk to Fisherman's wharf) and the price was okay $240US a night if i recall correctly.
San Francisco is a beautiful city, you are really going to enjoy your visit! August is the best month to go as the weather can be pretty unpredictable and surprisingly cold in the other months. The fog is incredible. I suggest you consider one of the Hop on Hop off buses for your initial days. They go to all the major tourist sites, you can hop off as long as you like and explore. Buses come by every 30 minutes.
https://www.city-sightseeing.us/tour/san+francisco/sanfranciscodoubledeckerbustour
A few places you should visit:
- Alcatraz
- Redwood State park
- Napa valley
- Fisherman's Wharf / Pier 39
- Lombard street (try walking uphill)
- Chinatown
- de Young Museum / Japanese Tea Garden / Golden Gate Park
- Alamo Square (famous hippie park, beautiful victorian homes)
- Nob Hill at night
If you are a military buff:
- The Presidio
- Battery Spencer / Battery Kirby
- Fort Point
I agree that renting a car for a day or two is a great idea. I drove the Pacific Coast Hwy SR1 southward to Carmel.