There's plenty of places to eat on the street in Thailand, this is one of my favorite places in Bangkok: Phra Pradaeng, (pronounced like pa-pa-dang). This area along the river, under the bridge, has some fantastic seafood eating places. They're only open during the evening, the food is fresh and the prices are low. There's also a nice clean market there, I like to go shopping at, in the evenings.
As you walk along the river, you will see little sitting down tables, with customers sitting cross legged on mats, and ad-hock kitchens in the open air, or under a make-shift canopy. It's not fancy, but don't let that put you off. We sit like this at temples all the time, it's all part of the Thai experience.
I set off from the the Supalai building, which is nearby so it was a taxi ride there, if you're on the other side of the river, there is an all day all night boat crossing, 2 baht during daytime and 3 baht in late evening.
Don't worry about ordering, they have photo-book menus, you can order by pointing at the photos. The meal at the top cost me 540 baht, that's about $16. Including sour fish, huge barbecued shrimp, spicy cashew nuts, fried greens, and stir fried rice.
To find Pra Pa Dang, see the map below.
View Phra Pradaeng in a larger map