Why isn't 到 (dào) used in 某天我去北京?
First, grammars of Chinese and English are totally different, you don't need the preposition like in English.
Second, in my opinion, 去 indicates that you start the action of &quot;going to a place&quot;,and &quot;到&quot; indicates that you have finished that action, so you &quot;reach a place &quot; or &quot;arrive at a place&quot;.
An example:

本周二我会坐火车去北京，周三到。
I will  go to Beijing by train this Tuesday and I will arrive on Wednesday.