Hello The sentence structure you are looking for is (으)ㄹ까요 This is attached to the ver at the end of a sentence and is used when you want to suggest something i.e. shall we, do you want me I'll give you some examples Where should we go eat? 어디에 먹을까요? Should I help you?/Do you want me to help you? 도와줄까요? Shall we go to see a movie tomorrow? 내일 우리 영화 볼까요? Hope this helps ^^

밥먹으러 어디로 갈까? for your friends. 식사 하러 어디로 가시겠어요? for your priority. It's an honorific expression.

Hello :) I'm Ellie! I'm sorry, but I think first answer is a little bit awkward for me. Shall we go to see a movie tomorrow? 내일 우리 영화 볼까요? Do you want me to help you? 도와줄까요? or 제가 도와드릴까요? They are right but, 어디에 먹을까요? It feels awkward for me. Anyway, Where should we go (to) eat? Should is kind of strong suggestion in English right? You can say, Where should we go to eat? - (우리) 어디 가서 먹는 게 좋을까요? / 어디 가서 먹어야 할까요? / 어디 가서 먹을까요? - (우리) 어디 가서 먹는 게 좋을까? / 어디 가서 먹어야 할까? / 어디 가서 먹을까? Where should we go to shop? - (우리) 어디 가서 쇼핑하는 게 좋을까요? / 어디 가서 쇼핑해야 할까요? / 어디 가서 쇼핑할까요? - (우리) 어디 가서 쇼핑하는 게 좋을까? / 어디 가서 쇼핑해야 할까? / 어디 가서 쇼핑할까? Where should we go to see a movie? - (우리) 어디 가서 영화보는 게 좋을까요? / 어디 가서 영화봐야 할까요? / 어디 가서 영화볼까요? - (우리) 어디 가서 영화보는 게 좋을까? / 어디 가서 영화봐야 할까? / 어디 가서 영화볼까? First line is polite way for elders / Second line is impolite way for friends. I didn't just translate, I gave you normal expressions when we talk about them in normal conversation. You can choose anything you want. It's little bit different, but just has almost the same meaning. (Third one is closer with 'Where will we go to eat' but It's more formal I think :) ) I hope it will help :)