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

Answer: 
Maybe you're looking for the word "**eatery**".

> 
> One of the best eateries in town.
> 
> 
> 

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**
A restaurant, a diner, an eatery, and a café are all places where people go to eat meals.