Yes, definitely Balboa Park. You might enjoy the Museum of Man, which normally has really cool exhibits, or the Air & Space museum. The Natural History and Science museums are also good. I love the movies on the big screen at the Science museum. You can also easily visit the SD Zoo, which is also in Balboa Park. If you want to eat there, the Prado is a nice restaurant.
Outside of Balboa Park, my fav restaurants in San Diego are Born & Raised or Cowboy Star for steak, Juniper & Ivy or Trust for new American, Sushi Ota or Sushi Tadokoro for Japanese, Menya Ultra for ramen, Crack Shack for fried chicken, Jayne's Gastropub for casual British pub food, Oscar's Mexican Seafood, The Taco Stand, or City Tacos for tacos, and Las Quatro Milpas for OG Mexican like your abuela makes (cash only).
Enjoy our beautiful city!