SF restaurant for group of 15
that's a tough budget to stick within in that neighborhood once you throw in alcohol...E&O Trading Company is close to that intersection and I think you can probably stick within your budget. i've been there for groups that size but it's been a few years so i can't remember the noise level.
You can contact Le Charm and let them know the number of people and your budget. They have a covered/heated patio that can accomodate larger parties and can work out a menu in your budget.
Le Charm French Bistro
315 Fifth St., San Francisco, CA 94107