Hope you will have a great vacation in San Diego! It IS "America's Finest City", after all. (Ok, so I might be a little biased since I live here.
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I would definitely recommend a day at the San Diego Zoo! The pandas are worth seeing - if you go first thing in the morning down to where the pandas are you usually don't have to wait in line, and can stay as long as you want, rather than feeling you need to shuffle on through to let other people have a chance. I really enjoy "The Wild Ones" show in the Hunte Amphiteater - it's about a 20-minute show that features interesting critters (like wolves, binturongs, servals, cheetahs, hawks or hornbills) performing natural behaviors.
The Zoo is in Balboa Park...and you can spend days in Balboa Park itself if you visit all the museums! The Natural History Museum is very nice (there's a fee), and there's art museums, an aerospace museum, the Museum of Man...lots of places. You can also visit several gardens (those are free) like the Rose Garden (my favorite) or the Scultpture or Alcazar Garden. In Spanish Village there's a little art colony - there are painters, sculptors, potters, etc.
Old Town can be interesting, if you're interested in old California history, but it's also quite touristy. There's also the Mission San Diego de Alcala - the first mission established by the Spanish monks.
Seaport Village, which is downtown near the Convention Center, is a fun little shopping center to wander around, and also has some decent restaurants...and there's a Ben and Jerry's ice cream place there.
If you want to try some "local" fare, visit Rubio's and have some fish (or shrimp or lobster) tacos. Rubio's is a chain and they're all over the place now. Or Roberto's (lots of those, too) for more standard Mexican fare. Those are both take-out places. There's tons of good restaurants in the Gaslamp District downtown - just about anything down there is good. Old Town Mexican Cafe is good, too - try the carnitas plate. Most of the restaurants in Old Town are fine. If you like Thai food, there's a place called "Saffron" on India St (near Old Town) that's very good...it looks like a little hole in the wall, but the food is yummy, and not hot and reasonably priced. And there's an Italian gelato place next door.
The El Prado restaurant in Balboa Park is good, too.
For breakfast we like the Original Pancake House, which is in Linda Vista/Kearny Mesa. It's a little pricey, but the food is excellent - and they use *real* silverware, not stainless. They have a HUGE apple pancake, as well as potato pancakes, crepes, buckwheat pancakes, waffles, french toast, omelets, etc.
You might want to drive over to Coronado Island - there's a very nice beach there near the Hotel del Coronado, and it's interesting to see the Hotel del!
La Jolla Shores is a very nice beach. Someone else mentioned going to see the seals in the Children's Pool at La Jolla Cove.
If it's a clear day, the view at Cabrillo Monument on the end of Point Loma is gorgeous. At the Visitor Center you can learn about the founding of San Diego by Juan Cabrillo, and then walk to the old lighthouse. It's run by the National Park Service, so there's an entrance fee unless you have a National Park Pass or Golden Eagle.
If you want to do a little hiking, Torrey Pines State Park has some nice (and short) hiking trails, though most of them are a bit hilly. The hike down to the beach and back is very nice.
As for the weather - it's about as good as you can get! In September it's most likely to be in the high 70s and sunny along the coast during the day,
though it does get much warmer inland (80s or 90s), but most of the "touristy" things are close to the coast where it's cooler. If we get a weather condition called a "Santa Ana" (which is common in September) then it could get up into the 90s on the coast. The saving grace of the Santa Anas is that the humidity drops to 20% or so. It almost NEVER rains in San Diego in September.
I'm not a night person, so I really can't suggest any "Girl's Night Out" types of places...though the Gaslamp District downtown is quite a night spot.
Hope that helps!
Laura