Elle Tha Pra Chan
This is one of the few decent restaurants and bakery near the Grand Palace. It doesn't have an English sign on, but it's not that hard to find. Menus are in English, and have pictures shown with them, so just point to the dish of your choice. It has the typical Thai dishes as well as some Italian pastas. Many art students from Silpakorn University have lunch together here, so expect it to be very crowded and noisy around noon.
Krua Khun Kung
Tucked in a small alley, this restaurant is the only good restaurant close to the Grand Palace. Its odd location makes it often unnoticed by foreigner travellers, which is a shame as it has a great view over the Chao Phraya River. It's best to sit outside on the terrace, but you can also sit indoors if you want to cool down from the heat. On the menu is seafood, and some of the best the city has to offer. But beware: it's very spicy!