It may be possible to find a 4Br in the Mission for that about that price range.
The mission is a hot spot in SF. This rental market is pretty competitive, great places get rented up very quickly!
Feel free to contact me anytime with your real estate questions.
Hope this helps!
A 4 bedroom place in the Duboce area is going to be hard to come by for that price. Rents are closer to $5-6K/month. If you go to Vanguardsf.com and click on the link for "Agents", Craig Waddle can help you with your search, he's in charge of or property management division