"-로" is used to put an emphasis on "direction" while "destination" is stressed, then "-에" is used rather than "-로" 해변으로 = in the direction of 해변 해변에 = to 해변(focused on 해변 itself as destination) "verb + -(으 or 하)러" is totally different from "noun + 로" and "에". It means "in order to do something". 나는 7시에 갑니다. where? ☞ 직장에 = to my workplace(your destination) for what? ☞ 일하러 = in order to work(the reason why) \^o^/

As you know, 어디로 is 'where' 'where to go' (place)~로, ~으로 So, 해변으로 is correct. ex) 도서관으로(to the library), 학교로(to the school), 방으로(to the room), 버스정류장으로(to the bus stop), 쇼핑센터로(to the shopping centre) and so on. ~하러, ~러 is doing something. 일하러 is correct. ex) 마시러(to drink), 자러(to sleep), 걸으러(to walk), 수영하러(to swim), 운동하러(to exercise) and so on.