You can also try flying into SJC(San Jose Airport) and then book your hotel separately. From San Jose Airport the best way to get to San Francisco is take 880 South(Follow signs for 880 South Santa Cruz and you will be brought right onto the freeway) then 280 North by Stevens Creek Blvd(stay in the right lane as it can get a bit confusing). About a 1 hour 15 min trip.

SFO can have fog delays.

SJC has easier customs clearance as its smaller than SFO and you can visit the Silicon Valley(Google,Facebook) and other cool places then go up to San Fran.

If the fare is less expensive this may be your best option.Plus the rental car center is located directly opposite Terminal B just down the way from the International Arrivals building.

When you return your car you can do it 3 hours before your flight and TSA lines are generally not bad at SJC. If you see that the Terminal A lines are long walk 5 minutes to Terminal B and then turn right to the International Departures area.

The CLUB@SJC offers lounge access for $35 if you do not have business or First Class but is included with BA First or Business Class.

SJC is my hometown airport and they have some good restaurants in Terminal B(Pizza My Heart) Tres Gringos in Terminal A. Britania Arms(British Pub) and Peet's Coffee has good coffee.

If you don't want to rent a car you can take the Free VTA 10 Bus to the Santa Clara Cal Train and take Caltrian to the City or take VTA 10 to Light Rail into Downtown San Jose and have Enterprise prick you up and they can drop you off at the airport there is a branch on Stevens Creek Blvd near Valley Fair Mall in Santa Clara and there may be one near the Downtown Area to avoid any airport taxes.

Uber is also another option.

Good luck and Cheers!!!!!!!!!!