If you can somehow swing it, going to Vandenberg Air Force Base might be interesting. But they have become very strict about who gets let on the base.

Like you mentioned there is the mission which should be really beautiful after all the rain we got. There are some animals you can pet, but they are shy. The Ox is a big sweety if you can convince him to come to the fence. Pro tip, don't park at the main entrance. It costs money. There is a back entrance that lets you walk on an old dirt road and gets you in for free. At one point it splits into two roads, so one you can take there and one you can take back. It's a little bit of a walk but it should be very beautiful. I highly recommend leaving before sunset though, as the mission is right on the edge of civilization and predators are known to be in the area. If you use the main entrance you can stay longer, but if you use the back entrance it gets a little scary.

There is a place called the "Wine Ghetto" which is a section of town full of different tasting rooms. If you like wine tasting but don't want to drive around all over the valley, that's a decent spot to go to.

There is the Chaperal near Vandenberg Village. It's a shrubby/woodsy area above the town. Nice hikes through there.

Cabrillo High School has a small aquarium which I've heard is decent.

If you are looking for more touristy stuff, I'd swing over to Solvang. More shops, restaurants, and another mission. However depending on which direction you are coming from, is a good 30-45 minutes away from Lompoc.

I can't really think of any good places that have notable desserts unfortunately.

For Mexican food I recommend San Martins for their chips. It's very low key and usually not packed except for Taco Tuesday. Otherwise Florioanos(?) I've heard is amazing.

There is a movie theater but they only play small time films.

There are a couple of good bars to go to if you are into that. Shamrock is my personal favorite.

Scratch Kitchen on H street serves local wines. The food is good but I just can't really describe what kind of food it is. It's just good wine food.

Los Olivos, Buelton, Los Alimos, and a few other small towns are cute little places to stop at too. Nice little shops, tasting rooms, and small town charm. Beulton also has Pea Soup Andersons, a fun place to take kids to but also has great food.

Dong Hae has good Japanese food. There is an Italian restaurant on H street which is eluding me. Plenty of fast foods as well.

If I can think of more I'll add on to my comment, so check back often.

Harris Grade is a curvy road with a great view of the valley. There are areas you can pull off to the side and take in the view.