Just an update. I decided to just book something closer to the airport. Just decided on today's Hotwire express deal. 4 star hotel near SFO - Burlingame Area for USD 138/night. Used the link, got $USD10 off, for a grand total of USD162.
I ended up with the Westin, which I'm quite happy with with the free shuttle and all. It's going for about USD200 on booking.com.
I don't know if it's useful, but I made a screenshot of amenities shown, but not sure how to add it.
Either way it showed "Airport shuttle, Business center, Fitness center, Indoor pool(s), Pet friendly, Pool(s), Restaurant(s), Self-service laundry, Smoke-free rooms" at the pre-booking page and "Pet friendly, Indoor pool(s), Airport shuttle, Smoke-free rooms, Fitness center, Pool(s), Restaurant(s), Business center, Self-service laundry" after booking.