来 / 去【lái / qù】

来 is movement towards the speaker, 去 is movement away. Which one you use depends on where you are standing, not on where the movement ends.

The place follows directly

No preposition. wǒ qù我去dào到Běi jīng北京 is wrong; 我去北京 is the sentence.

Purpose after the verb

A second verb after 来 or 去 says what the movement is for.

Both in one sentence

来 and 去 also attach to another verb to show which way it goes: 进来, 出去, 回来, 上去.

回, 到 and 去

回 is going back, 到 is arriving. 回家 is to go home, 到家 is to get there.