I agree basically with Eastbay1K, take the Amtrak Thruway bus from OKJ. The Amtrak site shows a stop at California and Drumm (SFF) which is next to the Hyatt Regency and Embarcadero Center Bldg. #5. If that stop is made by all Thruway buses, that's the one to use. There would be cabs available at the Hyatt for the short run up the steep hill (from Montgomery St, westbound) to the Fairmont.

IMHO, that walk is quite safe, at night, but also quite steep the last few blocks. While it could be a fun, daytime family excursion, not one at night when your goal is to just get to the hotel.

P.S., after noticing OP's just-made last post: not sure if the Uber fare quote is accurate. There would also be a $5 Bay Bridge toll.