We will be there for approximately 3 days and we are trying to decide between LaJolla, Carlsbad or Downtown. We are a family of 4 (2 boys 13 and 12). If there is a specific hotel recommendation please share that as well.

Carlsbad is my favorite

We have stayed at Pacific Beach several times. At the Catamaran and on the main beach at the Blue Sea Hotel. It is a busy area but fun. Next time, I’d like to try Coronado for a stay. Blue Sea is part of Pacifica Hotels. They also have a place in La Jolla and sometimes have deals on their website.

https://www.pacificahotels.com/hotels

For three days, it really depends on what you're planning to do. If most of your time will be spent in or around the downtown area, stay there or La Jolla (which is not a separate town, but is a suburb of San Diego) to minimize your driving time. Also, gas is expensive here! Carlsbad is lovely, but I-5, which gets you into San Diego, is always very busy these days. Taking the Coaster would be an option from Carlsbad and there is now a Trolley line that ends at UCSD in la Jolla. Those would be great if you are planning to visit the Embarcadero area where the USS Midway is, but not so great for Balboa Park and the Zoo. The Trolley would also be good for Petco Park.

The hotels suggested by MichelleY look lovely.

When will you be visiting?

We like Coronado and La Jolla

But yes, it depends on what you plan to see and do. Carlsbad is not especially convenient to Sea World, The San Diego Zoo etc.

Mission Bay area of San Diego.
Pacific Beach.

I like Mission Bay and Pacific Beach too. There is a Best Western there we have stayed a few times- right on the beach.

Another vote for Pacific Beach. We especially recommend the Catamaran Resort mentioned above. In addition to being a really nice hotel they have little areas set up with parrots and other birds which is fun for kids. It also has great add on activities-renting kayaks and a vintage paddlewheel boat you can take on a sightseeing tour of Mission Bay, etc.

https://www.catamaranresort.com/spring-activities

Coronado is great, but it may feel slightly more removed from the rest of the city so it makes it longer to visit places like La Jolla for example. La Jolla is nice as well but IMO I think Pacific Beach feels much more family oriented, and had the advantage of being more central.

like others said, it depends on what you want to do and what you are looking for. I've been to San Diego several times and have always stayed downtown. It's convenient to the Gaslamp Quarter, Balboa Park, Seaport Village and also to Coronado Island. Not sure how good my hotel information would be as it's been about 6 years or so since I've been but in previous trips, I've stayed at the Marriott, the Hyatt and the Omni. I would recommend all of them but my favorite was the Omni.