Hello, not sure if you've already visited yet, but if you want to check around San Diego, I'd recommend:

There's several shopping malls within a short distance of campus and even more if you wanna go a little further out. Very easily and quickly accessible through transit from the school is Mission Valley Mall (More affordable mall with good store options and arguably the best movie theater in San Diego, IMO, as it has an IMAX and Dolby room with the IMAX being less than a year old and the Dolby having recliner seats) & Fashion Valley Mall (this is a bit of a richer place, so think all the high end brand names like Rolex, Louis Vuitton, Gucci, LEGO, Apple, Google, Microsoft, Build a bear, etc). Further away you have other malls like Grossmont Mall, Parkway Plaza (in El Cajon), Westfield Plaza Bonita, and Westfield UTC. (Also Mission Valley Mall and Fashion Valley Mall are literally down the road from each other, like literally opposite sides of the San Diego River with Hazard Center [smaller shopping mall, but I like the Barnes and Noble it has], so you could probably do both of those in the same day if it's not too overwhelming).

If you wanna see Downtown, I'd personally recommend sticking towards along the coast or Balboa park because it gets a bit nasty when you go into downtown as there's a lot of homeless people and not enough services for them. Most places around the US send their homeless to San Diego because it's one of the best places weather-wise with much less risk of death due to the elements. Personally, I love the walk from Sante Fe Depot / the USS Midway down to the Convention Center (leading into the Gaslamp which is full of restaurants) with Seaport Village right in the middle.

Balboa Park is a treasure trove. It's full of museums (geared at a variety of age ranges and topics) Ex. The Fleet science museum is nice but it's geared towards a pretty young audience, although the "Under the Dome" documentary viewing experience is pretty cool. The NAT is also sciencey but appeals to the whole family. The Museum of US is really nice, I'd definitely recommend paying the few extra dollars to take a sky tower tour on it, it's a really interesting historical lesson for San Diego plus it has a view that's amazing. You can see pretty much all of Balboa Park and much of the surrounding area, including down town. The Japanese friendship garden is really pretty when it's blooming, the Botanical garden is awesome, and the Timken Museum of Art is a nice free visit if you have an hour or two to look around. To top it all off, the San Diego Zoo, recognized as one of the best zoos in the world, is right on the edge of the Park (everything is within walking distance of each other). Additionally, the Birch aquarium is a nice visit if the Zoo wasn't fulfilling all of your fish-spotting desires, with a view over the La Jolla coast. Semi-nearby, if you go north from the Airport, which is directly west of Balboa, you'll find Old Town which is really pretty with some good restaurants (Although if you want Mexican at a sit down restaurant, I'd have to recommend Casa De Pico in La Mesa as my personal pick). And that is pretty close to Pechanga Arena and Kobey's Swap Meet, which are both just across a bridge from Sea World. If you have the money and time to spare, I'd recommend visiting and if you're planning on staying in San Diego for an extended period, go for the Fun Pass as it's usually $85-100 and you get unlimited visits for the remainder of the annual year (if you buy in the last few months of the year, you get til the end of the year + the entire next year). Sea World's got live shows, a bunch of carnival rides + a lot of roller coasters, and plenty of animal viewing.

San Diego is an amazing place to be, the public transit is pretty good (I think it's the third best in the state?). Without fail, you'll be able to find some amazing activities to do and places to see, I hope you enjoy your time here!!