need a place to live in SF

I love my home, but it's time to move on. Fox and I are looking to move to SF. Here's what we're looking for:

These are non-negotiable:
*2br
*hardwood floors (or other uncarpeted option)
*takes cats
*laundry in or next to building (prefer in building)
*no bugs/vermin
*decent landlords/neighbors
*parking in-building or available nearby
*good transit options - prefer Mission or Castro

These are strong wants:
*gas stove
*backyard (can be shared) and/or balcony
*near cool stuff
*low mold (is this even possible in SF?)

Can you help? Do you know a landlord looking to rent, or a friend who is moving out or has a space in their building?