I would recommend downtown, Crown Point/Mission Bay or Coronado as a location not to far from either attraction. Crown Point is right next to Sea World and on Mission Bay which has a sidewalk and a few playgrounds right along the bay. Check out
http://www.paradisepoint.com/Paradise_home.aspx. This would put you 5 minutes from Sea World. Dowtown San Diego is pretty fun/touristy and very close to the zoo - maybe 10 minutes. Coronado is probably 20 minutes from the zoo and 30 from sea world. The Hotel Del is one of a kind (make sure you go there and have lunch and/or drinks on the deck) but the Lowe's Coronado may be more of a kids vacation spot.
I lived there for years and I really really miss it...
Have fun!