this trip I took the city bus 80% of the time ,

It helps that the 3 places I needed to go were right on the bus route , but its easy and cheap, 8 baht to less than 20 baht,

The #40 bus from Sukhumvit to Chinatown will drop you off in the center of Chinatown, where if you take the underground Metro MRT the last stop is the train station Hua Lamphong and its a pretty long walk into Chinatown,

here is the route list
http://www.transitbangkok.com/bangkok_bus_routes.html

You need the route number as the destinations on the side of the bus is normally only in Thai script .

Its one way to see the city , just try and go mid day as it can get crowded if you are going the direction of the office workers.

Have fun

Rally