Indeed, there are many words for "dining place" in Korean and they all seem to have slightly different nuances. FYI:

1) 레스토랑 = restaurant

Literally, mean restaurant yet many Koreans usually associate 레스토랑 with some expensive places, often serving western or western-Korean fusion rather than orthodox Korean. For example,

I had a date with her in a restaurant. = 나는 레스토랑에서 그녀와 데이트 했다

http://bit.ly/2BSiN7d

2) 음식점, 식당 the very neutral word for eating place - can be upscale or humble, safest word to use as it can be used for all occasions

http://bit.ly/2FHwCb7

3) 구내식당 = canteen (in a school or a company)

http://bit.ly/2DXMben

4) 학생식당 = school canteen

http://bit.ly/2BSj8qB

5) 분식집 = 분식점 = snack bar, snack place

분식 means snack in Korean yet you can still have a proper meal in reality. Usually small and humble, good value for money places targeting young rather than old.

http://bit.ly/2EDgyrm

6) 가정식 = 집밥 = homemade meal

집= house, home

밥 = cooked rice or meal

저는 집밥을 가장 사랑합니다 = I love the homemade meal most.

우리 같이 밥먹자! = Let us have a meal together (casual form, suggesting for a meal together)

같이 = together

7) name of dish + 집 = > eating place with some clear focus in terms of menu etc.

For example,

• 피자집 = a pizza place
• 국수집 - a noodle place
• 도시락집 = a lunchbox place (도시락=lunchbox) http://bit.ly/2DXFWLr
• 햄거버집 = a hamburger place (ex. 버거킹)
• 빵집 = bakery (빵+집)
• 치킨집 = fried chicken place http://bit.ly/2nye2eU
• 중국집 = a Chinese food place (This is the one and only exception as there are no other examples as such. For example Koreans never say 미국집 nor 일본집)

일본집(X)

일본 레스토랑 = 일본 음식점 = 일식당 = Japanese restaurant

http://bit.ly/2s7Z3x8

P.S: I inserted some GOOGLE image search results as it helps one to understand what a word or concept exactly means in the native's head. ;)