Not sure what your stance is on community style apartments, but this guy checks off just about everything on your list, except maybe the yard. Had a couple friends that used to live there with 2 big dogs though, and they had plenty of space in the house for them and there's plenty of open space around the property for walks and things like that.
My friends also had to break their lease and I don't think it was anything too outrageous.
Check this one out. This was the most expensive option and still within your range:
Best of luck!