Is it possible to rent a furnished room in Nob Hill?

Yes, you can probably find a furnished sublet in the area. There are local universities (like UCSF) and it is not unusual for students and instructors to rent out there rooms while they are on leave for a semester. Usually they will be furnished.

Cost is another issue. Nob Hill and especially Russian Hill are very expensive. A typical one-room apartment will run $2000/month. You can find slightly better deals just east in North Beach.

If, however, your son doesn't mind taking public transportation into his internship for 15 to 20 minutes, I would recommend looking for an apartment in the Richmond District to the west. Very foggy, but much cheaper.

Good luck with the apartment hunt.