The Café Amazon is a small coffee shop that is very popular in the area. Its not far from the BTS located in the Phra Khanong area of Bangkok. Note that the coffeeshop is located in the PTT Park in Rama 4. There are a number of other coffeeshops in the area and also hotels. The coffee shop has outdoor seating if you wish to have your coffee outside and also offers WiFi.
There area a number of hotels in Bangkok located in the area such as the Jasmine Hotel amoungst others. See the rest of the website for more details on the area from the top menu. See other coffeeshops in the area listed here.