Thailand has a large number of indigenous restaurant chains offering much the same fare as your average street stall, but with the added advantages of air conditioning, printed menus (often in English) and some semblance of hygiene. All the chains are heavily concentrated in Bangkok, but larger cities and popular tourist spots may have an outlet or two.
MK and Coca are near-ubiquitous chains specializing in what the Thais call suki, perhaps better known as "hotpot" or "steamboat". A cauldron boils in the middle of your table, you buy ingredients (10-30 baht a pop) and brew your own soup. The longer you spend, the better it tastes, and the bigger the group you're with, the more fun this is!
S&P  outlets are a bakery, a café and a restaurant all rolled into one, but their menu's a lot larger than you'd expect: it has all the Thai mainstays you can think of and then some, and most all of it is good. Portions are generally rather small, with prices mostly in the 50-100 baht range.
Yum Saap (signs in Thai; look for the big yellow smiley logo) is known for their Thai-style salads (yam), but they offer all the usual suspects as well. Quite cheap with mains around 50 baht.
Kuaitio Ruea (signs in Thai; look for the boat-shaped decor and hungry rat logo) does dirt-cheap noodles with prices starting at 25B. Portions aren't too generous, but at that price you can get two! No concessions to English speakers in menu or taste, so point & choose from the pictures and watch out for the spicier soups.
Fuji  and Zen specialize in surprisingly passable Japanese food at very cheap prices (at least compared to Japanese restaurants almost anywhere else); rice/noodle mains are less than 100 baht, and you can stuff yourself full of sushi for less than 500 baht.
And yes, you can find the usual McDonalds, KFC, Pizza Hut, Komalas etc if you insist. If you do end up at McD's, at least try the un-Maclike fried chicken with McSomTam (green papaya salad). For those craving American-style pizza, try the ubiquitous The Pizza Company, which is a less expensive and (arguably) tastier local chain.