All good suggestions so far.

I would add the following.

The WAP is now called San Diego Zoo Safari Park. It's in the same place and has the same stuff.

In my personal experience, the Gaslamp has changed from an all-ages destination [read: stuff for mature folk] into a thumpa-thumpa music clubbing scene, appealing mostly to the younger crowd.

There are innumerable fantastic craft breweries, both in San Diego proper, and in "North County" (Carlsbad-Vista-San Marcos).

Speaking of North County, Cruisin' Grand in Escondido should be up and running on Friday nights by that time. A good showing of vintage cars of all breeds.
There are other weekly car gatherings in the county with which I am not as personally familiar.

My biggest warning to June visitors to SoCal is June Gloom.
Out-of-staters from four season climates like Minnarusta think that Spring is the time of sunny, green rebirth.

Not so, here.

June can be one of the dreariest months of the year.
The broken record weather forecast is "Late night and early morning low clouds and fog along the coast, turning into hazy afternoon sunshine."
West of I-5, the fog may or may not EVER burn off during the day.
Your stay at the beach will not be the same as a visit to the gulf coast of Florida.
And regardless of the level of grey, the ocean water is fresh from Alaska.
Go just a few miles inland, and the weather will be significantly different.

I don't mean to tinkle in your Cheerios, but that's June here.