Yok Yor Marina and Restaurant
You can sit at the open air terrace along the Chao Phraya River or inside with air-conditioning and live music. On the menu is seafood, including oysters, fish and shellfish. Most of the visitors are local Thais, at it is at the Thonburi bank, but more and more foreigners seem to get to know it. The only downer is the karaoke machine and loud TV, sometimes used by locals ruining the atmosphere.
Ruam Tai
This is a typical street restaurant that is good for trying some Southern Thai cooking. You might want to consider the gaeng som, a sour and thick vegetable soup. Diagonally across is Dao Tai, another Southern Thai restaurant. Both of these restaurants only have Thai signs and menus, so you might want to use a phrasebook.
If you want to eat like the locals, or if you are on a budget, head for Wang Lang Market. The main roads and their side streets are filled with plenty of unnamed restaurants and simple carts selling meals for less than 50 baht. It is known as one of the best places in Thailand to get food from Southern Thailand. The story goes that Southern Thais settled in this area as trains from the south used to arrive at the Thonburi Train Station nearby.
The Bang Ramat area has plenty of cheap budget eateries as well, very convenient in case you're waiting at the Southern Bus Terminal. Just walk down Phuttamonthon Sai 1 Road and you will find plenty of restaurants, especially at the intersection with Ban Suan Phutthamonthon Road and the intersection with Wat Kaeo-Phutthamonthon Sai 1 Road. They offer traditional Thai cuisine, Thai and Western-style desserts and refreshments. Most delicacies on sale won't cost you more than 25 baht.
Central Plaza Pinklao is a good alternative if you're looking for mid-ranged chain restaurants, such as Yayoi and Sizzlers, or even the usual Western fast food chains. If you're elsewhere in Thonburi, hawker stalls are all over the district, as are 7-Eleven convenience stores.
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This cheap restaurant is highly recommended for its cheap menus and great view over the Chao Phraya River. When it is dark, Bangkok's highlights along the river are well-lit, such as the Grand Palace, Wat Arun and Wat Kalayanamit. Ordering goes by "self-service", which means you must walk to the counter yourself and order what you want to have. This is fairly straightforward as the menu is in English. After it, you have to pick up the glasses from a shelve and fill them up with ice cubes if desired. Some good dishes are the fried rice with maggie sauce or the fried rice with Thai chili paste and fried chicken. If you have a big appetite, also order the fried minced shrimp cakes. It's good.