Wow- $300 isn't much of a budget for So Cal. Having said that- if you are not planning on camping- what you might do is pick a hotel that is near Disneyland in Anaheim. You can often find great deals in that area- some as low as $49 a night, some with continental breakfasts.
You won't have a fantastic hotel, but those will run at least $100 a night if not more, anywhere worth staying in So Cal. If you stay in that area, You will be in a decent part of town with lots of other people- safer that way. (There are some great areas in California and some pretty dicey ones).
Then- you can go to free places like Dana Point Harbor. They have a nice walking trail and sand area. you can rent Kayaks to play in the harbor. There is a marine life museum and a pirate ship at the end of the park.
The next day- you can travel up PCH (this is Pacific Coast Highway 1) up to Malibu. Might run into famous people on the beach or in one of the little bistros. Take a nice walk on the beach and watch the sun set over the ocean.
The other option is to go south on I-5 to San Diego. Visit Old Town for the day. Great art shops and fantastic authentic Mexican food! Not pricey either.
One other tip- there is a fantastic boutique hotel in Dana Point called the Blue Lantern. The rooms can often go for upwards of $400- but- they run a lot of specials. They are right on the water perched on a cliff with amazing coastal views of the harbor. The street is a dead end so there isn't any traffic noise. The rooms are wonderful and have fireplaces...very romantic. They have a delicious breakfast that comes with the price of the room and wine, cheese and other goodies in the early evening...all free. They have beach bikes you can use to take a ride around Dana Harbor. If you let them know it is a special event (like an anniversary) they will have a little welcome surprise in your room.
Here is the website-
They had a secret deal going last year- if you call up the day before and say "carpe diem"- they would give the room for half price that night. So you may get the hotel in Anaheim and then spend one night there- that would keep you relative to your budget.
Have a great trip- if you want more info let me know :)