Cha-am is nice, about 2 hours drive from Bangkok. Depends on what you want to do, it tends to be a chilling on the beach / by the pool place. Hua Hun, a little further down has the town handy for markets and eating outside the hotel.
Don't bother with anti-maleria tablets, it is not a big risk at all in that area, and the pills often make people feel bad.
In theory you need to carry your passport at all times, but in my 13 years in Thailand I have never been stopped and asked for it. If you are concerned, have a photocopy handy, don't carry your passport on a night out on the lash.
Thailand is as safe as most places. The current political strife doesn't directly threaten tourists (although the airport closure was a monumental pain for some). The big question is want happens when the King passes away. Best guess is the country shuts down for a month, minimum.
btw, Amphoe is a local government subdistrict (very vaguely similar to a parish in the UK). Cha-am and Hua Hin are in Phetchaburi province