I lived in San Diego for years & loved the city. I have also lived on board my boat on & off for extended periods over my lifetime & it can be a fun experience.
IMHO, Minimum boat size for the two of you to be a comfortable live-aboard is going to be a 35 foot boat or bigger, I would estimate. Anyone can live anywhere for a short time, but for full time, long term & keeping comfort, amenities & storage in mind along with holding tank size, etc. , that would be my input from my personal experience.
42 foot trawler like a Grand Banks 42 or Kadey-Krogen 42 would be even better yet & a perfect compromise size trawler for a comfortable long term live-aboard home.
One draw back of living aboard a boat in a slip in Southern California is the slip rents & additional fees, specific type of insurance they require, survey expense to get that insurance & other expenses associated with being a 100% true live-aboard, Costs can be very high.
It is not cheaper than an apartment !
Most marinas allow you 3 nights a week to live on board with no additional fees. -- past that, there are often additional fees.
Sneak aboard is not a good long term approach as they can track your comings & goings easily with electronic gate key access records & plus seeing you there all the time, it can be pretty obvious. Then next thing you know your kicked out.
Many marinas I have talked to at Shelter & Harbor islands only allow 10% of the boats at the marina to be true 100% live-aboard. Of course varies with each marina.
Live-aboard's put a lot more wear & tear & clean up expense on the shared facilities like rest rooms & showers & add more hot water expense, parking issues, Electrical expense, etc. to the marina overall operation costs.
BTW - They also do not take well to people decorating the boat like a house with plants & such & Nothing can spread out & be on the docks.
Often you must be signed up & pay for & have receipts for a mandatory pump out service to be sure no one is discharging waste black water over board & must have a holding tank of sufficient size.
If your looking for a recommendation, I would say Chula Vista Marina is one of my favorites down in San Diego & does allow a certain large % of cruisers to live aboard, as many of the BaJa Ha HA group gather there every year up to 6 months before venturing off to Mexico every year on November 1st.
Wishing you good luck with this new adventure.