I suggest that you rent a car when in San Diego and this will allow you to find lodging out of the downtown areas of San Diego. And there are many nice places in San Diego that are reasonable, especially in the hotel circle area. There are also some reasonable places on Shelter Island, Point Loma and to a lesser degree the San Diego Airport area and La Jolla. Although possibly out of your prie range, is the Hilton at Harbor Island.
The DO NOT MISS sites to see are the San Diego Zoo and The USS MIdway (even if you are not into military related things). Other sites are Old Town, and the Gaslamp section of downtown San Diego.
San Diego is an excellent port city because the airport is 10 minutes from the cruise terminal; there are lots of places to stay, restaurants, and activities.