A lot of it depends on the type of person you are. When I was younger, I could sleep literally on a pile of rocks with no padding and still get a good nights sleep. Nowadays, I feel like I'm roughing it without a thermarest.

If it's a park, I assume it's going to be grass surface? Just throw a blanket down under your sleeping bag and you'll be fine. Or if you can get that eggcrate foam that'll work great. It's San Diego in May, not Alaska in the wintertime, so you don't have to worry about insulation as you would in colder climates, and even less so if you have a tent. The sleeping pad will be more for comfort than insualtion. If you do have some cold spots during the night, you can always throw some extra clothes under your sleeping bag for a little more padding.

Don't forget to bring a pillow. Most people aren't used to sleeping without it. A rolled up jacket or clothes in a stuffsack is better than nothing, but a regular pillow is a lot more comfortable.