Aire River is the best for nearby walks and the koalas in the campground. It can be heavy on the mosquitos and bogans side though, and can be full quite fast on a busy week end. Johanna beach is bigger and right next to the beach, but no koalas and less options for walks. Both are free and have (smelly) toilets. If you want to see all your options, download the Wikicamps Australia app for smartphones :
http://www.wikicamps.com.au/ . You can try Blanket Bay too, although I've never been there. It looks fairly close to the beach and quite large.
Regarding the 12 apostles area, there is no camping there, it's strictly prohibited. So you have to camp in the Otways or stay in town.