As you know, 어디로 is 'where' 'where to go'
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.