Depends what you consider inexpensive. I stayed at the Holiday Inn Bay Harbor. It is a short cab ride to the hotel from the airport. Holiday Inn is right across the street from the port. You can go to the San Diego Zoo, one of the finest, Balboa park has about 17 museums, there's Sea Port shopping area, Gas Light district, Coronado Island, and you can take a hop on hop off to a lot of these places.
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.
Old Town is very interesting. We took the trolley which is very close to the port. I always check hotel prices on www.hotel.com which gives me a great concept of the prices in all the areas. Hope this helps...