I am thinking that the level of hotel that has valet parking goes for significantly more than $200 a night in San Francisco. However, it is true that Xmas night is likely not to be a very busy hotel night, so maybe there will be special rates that get down to this range.

It is likely that there will be places open in Chinatown on Xmas night. You could stay in the North Beach area, it's walking distance to Chinatown. Bear in mind that most of the places on Grant Avenue itself are strictly for tourists, the more authentic places are on cross streets or on Stockton.