I just left San Diego last month- I worked as a traveler in the ER at Kaiser for 6 months. My company had my husband and I up in a condo in Mission Valley- a very nice area that is safe & centrally located to pretty much everything. This is where we stayed: The Missions at Rio Vista - San Diego, California
We have a dog, and this place allows pets. There are also several other very nice apartment & condo complexes in Mission Valley that are very nice, and Mission Valley is very close to Rady Children's (about a 10-15 minute drive, depending on traffic). San Diego is a beautiful place to be (I miss it already!). Let me know if you have any other questions!