We've stayed at the Best Western Seven Seas a few times and found it quite nice:
http://www.bw7seas.com/about-hotel.htm
It's in Mission Valley - walking distance to the Fashion Valley Mall, just north of the Zoo and Balboa Park.
I don't see anything on the website about pets, so I'm guessing it's a no, but you might want to give them a shout.
It's also at one end of a whole strip of hotels/motels. I think it's a great central location, just not close to the water.