식당 and 음식점 mean "restaurant" but the feeling is a little different. 식당 feels like "cafe" and 음식점 feels like "coffee shop". But really, the basic meaning is exactly same. I hope my explanation will be helpful to you :)

식당 & 음식점 both are restaurants. but.. 식당 is more of like cafeteria and 음식점 is more of like food store type of restaurant.. If you get what I mean...

식당 and 음식점 mean "restaurant" but two words are used differently to call "a dining room" 식당 is also used to call "a dining room" in a house. However, 음식점 is not used as "a dining room" in a house.