Kanchanaburi is located about two hours west of Bangkok. It is famous for being the location of the Bridge on the River Kwai, and has two large Allied War Cemeteries nearby. The province also has a lot of natural beauty, with rolling hills, waterfalls, and a railway that travels halfway through the province. There is a good amount of English spoken here, due to the tourist traffic.
It is not uncommon to see these country styled restaurants in Thailand. I think Thai people are a little confused about what "country" means when referring to music. Thai people refer to their folk music as "country", and that is the sort of music they usually play in these places. You rarely hear "country-western" music in Thailand, but I think someone saw a few cowboy movies, associated them to "country music", and we are left with places like the "Wyoming" (pictured above) or the "Apache Saloon". Admittedly, these places can be a lot of fun.
Naturally, the reason most people visit is to see the famous bridge. This is it. Despite what you saw in the movie, the main bridge was made of steel - there were other temporary bridges made of wood. The bridge is still in use today by the State Railway of Thailand.
Waterfall at Erawan National Park. It's very easy to visit most of the parks by signing up for a tour at any guesthouse. The guesthouse I stayed at had some sort of deal worked out where employees of the tour groups would work tables at the guesthouse (serving food), in exchange for the opportunity to tout their tours. The tours are generally less expensive than comparable ones in Chiang Mai.