The top 3 primary telecommunication companies in Thailand are True Move, Dtac and AIS, in fact all their services and prices are nearly the same, therefore you could choose whichever one you want. They not only work in the big cities, but also in the islands, plains and the countryside. A SIM card generally costs about 50 Baht, and then you have to top it with the amount of money you want to add, the service centers are all over the country, especially in shopping malls. To give you an idea, a SMS would cost about 2 Baht, and they also have 3G flat rate packages on offer all depending on how much data you want to purchase.
Most of the WiFi available in large hotels and restaurants are free, but some may charge you some money depending on their location. Most of the bars too have free WiFi, but they may ask you to at least buy a drink to sit at their location and use their WiFi. Thailand is also known to have an abundance of Internet Cafés, especially in the major cities. An Internet Cafe in Thailand may char from 0.5 to 3 Baht per minute, which is very cheap. They also offer snacks and drinks for the customers.