Point Reyes Hostel
They have private rooms and you should be able to get one if you go on a week day. As for food, I suggest finding a recipe you want to make, bringing the ingredients, and cooking it in the gourmet kitchen there. What could be more romantic than that?
I did a solo overnight trip here on my bike earlier this year and fell in love with the hostel (I had already fallen in love with Point Reyes many years ago)