I’ll third Hodad’s. I grew up in Ocean Beach and I don’t think I’ve had a hamburger quite like it anywhere else. Incidentally, if you’ve ever seen Almost Famous, OB might look familiar to you - the opening scene is shot on and around Newport Avenue, and most of the rest of the movie was also filmed in and near the neighborhood.
Apparently we’re assuming Soul Bros #2 is not a vegan. That said, another burger worth sampling can be found at Slater’s 50/50. It, along with previously mentioned Con Pane and Stone Brewery, are located in Liberty Station. The “50/50” moniker come from their signature burger which is half ground beef and half ground bacon.
I’m a San Diego expatriate (18 years there). I recommend walking around the Hillcrest neighborhood; there are some good eats, fun boutique shops, and even some bookstores left, as of 2005 (I recommend Blue Door Bookstore on Fifth Avenue – hope it’s still there!). Hillcrest is also the “gayborhood,” so there’s usually something arty going on as well.
The Chicken Potpie restaurant on El Cajon Boulevard is a classic: potpie, veggie, mashed potatoes and gravy, and dessert for $5.25 (2005 price). Good, hearty, grandma-made-it chow served in a big cafeteria by 80 year-old waitresses.
There’s a lovely path from Morley Park down (and then up) into Balboa Park’s rose garden and Reuben H. Fleet Space Center. BTW, Balboa Park is wonderful and the Zoo is in this southeast area. You’ll have to ask a local in Morley Park where the route begins.
And please, please, please have some exquisitely greasy nachos and a carne asada burrito in my memory at an Alberto’s, Norberto’s, Filiberto’s . . . you’ll see a lot of these “berto” hole-in-the-wall joints; these Mexican greasy spoons are what I REALLY miss in my new Land o’ Jersey.
My husband and I visited The Midway a couple of years ago and we really enjoyed talking with the volunteers. Especially the ones who say “I don’t usually tell people this…” 
I tell my husband that I wish they could all be my granddad.
On topic:
If you’re down by the stadium and hungry go to The Old Spagetti Factory. They have a deal where you get an epic shit-ton of food (we had leftovers!) and a souvenir glass - to this day I still use mine often. When we got the bill my husband and I looked at each other and said “That’s it?” Excellent food, excellent price, excellent service. I remember it was chilly in there though so bring a sweater.
Food historians and anybody who likes Mexican food should read Gus Arellano’s Taco USA for the full history of the -Berto’s phenomenon.
Beaches … duh …
San Diego has a ton of great breweries if that’s your thing, as well. Karl Strauss, Alesmith, Lost Abbey, Stone, and Ballast Point are some favorites.
There’s also a very popular disc golf course at the far end of Morley Field. If you forgot your favorite driver, you can pick up a new one at the Pro Shop there.
You could go museum-hopping just in Balboa Park and easily spend the whole day. I wouldn’t consider any of them world-class, but there is some really neat stuff to see in every one. The Model Railroad museum has some fantastic layouts, with mini-dramas of one type or another everywhere you look. (see if you can spot the shark in the swimming pool!)
Nobody’s mentioned Whale Watching?
I don’t remember their schedules, but the California Gray whales migrate between Baja and Alaska.
Incredible experience.
Coronado Island is cool, and they have an IKEA store if you’re into that kind of thing.