The Eurasia Cha-am Lagoon is a resort and residential comunity 3km north of Cha-am. It boasts of two free-form pools overlooking the gulf. It is free to the public and open 24 hours a day. A terrace restaurant is available and serves Thai food that will cost you 100 to 300 Bht. Beer and liqour will cost you more so you might want to bring in your own drinks. This place is seldom crowded so it's the best place to hang out and take a dip.
Cham-am Forest Park is a small nature preserve as parks go but it's still worth seeing. All-terrain vehicles are available for guided tours of the park. The rental ranges from 500Bht for half an hour to 900Bht per hour. There is also restaurant within the park.
The summer palace Phrarachanivet Mrigadayavan was built in 1922 for the King and members of his royal household. Held open for the public as it is no longer used by royalty, it lies south of Petchakasem Rd, about 9km from Cha-am.
It is a group of teak houses on stilts and a maze of walkways connect them. The rooms are airy and the walkways are raised. There isn't much information avaialable in English so you may want to hire an English-speaking guide for the tour.