Question: The word "dormitory" means "sleeping place". Is there any similar word for "eating place"?

Answer: 
There's also *refectory*: 

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> A refectory (also frater, frater house, fratery) is a dining room, especially in monasteries, boarding schools and academic institutions. One of the places it is most often used today is in graduate seminaries. It is derived from the Latin reficere: to remake or restore, via Late Latin refectorium, which means a place one goes to be restored. [Wikipedia]
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the root of which it shares with *restaurant*: 

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> Modern restaurants ... emerged only in 18th-century Europe, although similar establishments had also developed in China. A restaurant owner is called a restaurateur; both words derive from the French verb *restaurer*, meaning "to restore". [Wikipedia] 
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Oh, and of course *beanery*, *hash house*, *greasy spoon*, & *automat*.
Maybe you're looking for the word "**eatery**".

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> One of the best eateries in town.
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Also the phrase "**eating place**" is very common.

There are some other words that I don't think you're looking for them. But you can also check them out.

Other words:
***cafe***, **self-service**, **diner**, **bistro**, **cafeteria**, **canteen**, **brasserie**