I have not been in San Francisco for four years, but four years ago I do not think it would have been possible to find a room in your budget areas unless it would have been in some really run-down place in the tenderloin. You might try to look at some of the older tourist courts and motels on Lombard St. There is a Days Inn and a Travel Lodge on Lombard that generally have rooms in the area of $150/night. They are older places, with exterior entrances, but since all hotels must have disability accessible rooms I imagine they could accommodate your partner.

Nothing on Lombard St. is near a BART line. I imagine your partner can take the BART into the city and then get a taxi to Lombard.

As I am sure you are aware, San Francisco can be extremely challenging for people in wheelchairs. There are lots of hills and routes need to be planned with care.