As a Brit, but not a teacher, and using the Oxford Dictionary as my guide for the definition of "beach":
• noun a pebbly or sandy shore at the edge of the sea or a lake.
• verb bring or come on to a beach from the water. — ORIGIN perhaps related to an Old English word meaning brook.
The "East Beach" must be a pebbly or sandy shore at the edge of the sea or a lake.
The "East Coast" is an area of coastline on the East side of a landmass that may or may not have a beach (i.e. it may have high cliffs that fall directly into the water, without any significant beach).
1st sentence OK.
2nd sentence OK, apart from the spelling (restaurant)