The biggest is the
U.S.S. Midway which is now docked in San Diego Bay and be turned into a museum. The ship can be seen via a self guided tour, there are many planes on display, and the hanger bay has several different flight simulators. More at
http://www.midway.org .
The U.S. Navy takes up a lot of San Diego Harbor. In fact, one of the three aircraft carriers based in S.D. is usually tied up right across the bay from the
Midway. About a mile up the waterfront from the museum is the docks for the harbor tours. The northern tour takes you past the dock for the carriers, the North Island Naval Air Station (always busy), the submarine base and out to Cabrio Point. There is usually a lot to see going on. The southern tour takes you past the docks for the other ships (destroyers, tenders, etc.) on the other side of the Coronado Bridge. As far as I know there are no public tours anymore of the bases, but I haven't checked.
Also across the bay on Coronado is the Naval Special Warface Command and Silver Strand which is the facilities for the Navy's S.E.A.L.s. If you drive south along the Silver Strand you can get glimpaces of their training facilities; sometimes if you even just walking along the beach near the Hotel Del Coronado you can see them hauling their logs up and down the beach.
San Diego's Balboa Park contains a number of excellent museums as well as the San Diego Zoo. The San Diego Air & Space Muesuem has a fantastic collection of military and civilian aircraft. (The Balboa Park Museuems are the overlooked attraction in the whole city - it's a shame more people rush to Sea World and bypass these places).
If you're visiting in October, Miramar MCAS throws one of the largest air shows in the country. It's now a Marine base, but back when the Navy had it was made famous as the home of 'Top Gun' in the movie. Lastly, if you're driving from
Disneyland to San Diego you'll pass right through Camp Pendleton, the primary west coast training facility for the Marine Corp. You can sometimes catch views of exercises, helicopters and landing ships off shore during exercises. But, again, neither of these facilities offer public tours that I am aware of.