우리저희는 로스엔젤레스를 가고나서 한인타운에 있는 한국 식당에서 밥을 먹었어요.

A few things:
1. 우리 <-> 저 is a politeness mismatch. It's very important to stay consistent here :)
2. 가고 나서 is spaced, but it's also not the right grammar point to use here.
3. It's better to keep particles than to omit them if you are unsure.
4. 먹다 is one of those verbs that require an object. You can't just say 먹다 on its own.

우리저희는 한국 음식을 너무 좋아해서 너무 행복했어요.

음식은을 먹자마자 H-Mart에 갔어요.

로스엔젤레스에서 촣은는 맛있는 한국 음식이 많이 있어서 다음에또 갔을 때도 꼭 한국 음식 꼭을 먹어야 돼요.

촣다 X 좋다 O
있다 is an adjective here, so 에서 is incorrect.
Again, particle omission is bad (unless you know for sure what you're doing).

다음 여름 방학에는 서울에 가면 너무 촣아해좋겠어요.

When used for yourself: 좋아하다 is a general statement of fact. You are describing yourself as liking something. 좋아요 is the word to use for feelings of liking something.
This draws a parallel to the more general adjective + -어/아 하다 structure (although, BEWARE, 좋아하다 is its own word NOT 좋다 + -아 하다). When you have an adjective that describes a feeling or sentiment, using -어/아 하다 turns it into a more objective description, which is why as a rule of thumb you can only use the -어/아 하다 form when the subject is someone else (because you do not know the feelings and sentiments of another person, you can only describe it).