Since you will be living in UTC, the nearest DMV office is located in Clairemont, which isn't too far away.
Here is a list of DMV offices in San Diego:
DMV San Diego Department of Motor Vehicles Locations - San Diego BizMart Business Directory
The Clairemont DMV is next door to Home Depot, in Genesee Plaza. You can see it's location on Google Maps:
4375 Derrick Dr, San Diego, CA 92117, USA - Google Maps
The Clairemont DMV is a large free-standing building, with parking in front. Get there early in the morning, so you won't have to wait too long.
There are lots of fast food restaurants at Genesee Plaza (Jack in the Box is right out in front of the DMV), if you want to grab a snack while waiting.
In California, you only need to have your car Smog Checked once every two years. There is no full vehicle inspection required like you would find in states like NJ and PA. The Smog Test is very similar to an Emissions Test.
My recommendation is simply to drive over to the DMV once you are settled in (your car is still ok with it's out of state tags for several weeks), and register your car at the office. They will give you a document which needs to be taken to take to a Smog Check station within 30 days. Smog Check stations are located all over San Diego. Some are "Test Only" stations, and others are equipped to do repairs if needed. A Smog Check takes around 1 hr, and can be done while you wait. The cost of a Smog Check is around $30 - $50, and you can find discount coupons in many freebie magazines like the San Diego Reader (found outside most supermarkets). San Diego Reader has lots of coupons in the back of the magazine.
You will also need to obtain a CA driver's license. No driving test is required for people with current out-of-state licenses. You simply have to pass a written test. You can get the info you need at the DMV. You can also find Drivers License study manuals inside most San Diego public libraries.
Speaking of libraries, La Jolla has a great public library located on Draper St, near Pearl St. It is across the street from a bunch of tennis courts. This library is one of the best in all of San Diego.
As far as insurance, simply find an Allstate agent near UTC when you arrive, and have them switch to your new CA address. Your insurance rate should be fairly similar to whatever you pay now, and possibly even less. State Farm is another good insurance company, if you decide to switch at some point. State Farm gives discounts if you have multiple types of insurance with them, such as Auto and Renters insurance.
One thing regarding car repairs in San Diego, if you take yours in for minor work such as an oil change, some places (chains like Firestone, Midas, etc) also offer to do a complete free inspection of brakes, muffler, wheels, shocks, belts, etc. They may recommend unnecessary repairs, so use good judgment on your part when responding to their recommendations. You may go in for a simple $10 oil change, and then they also recommend changing your brake fluid, power steering fluid and transmission fluid and you end up spending an extra $300. Keep track (a log) of when these things were last done, so you know if they are needed again. If they ever recommend a major repair, you might consider taking it to another shop for a 2nd opinion. With that being said, I would still say that most of my experiences with car repairs in San Diego have been good ones.