Can I say 在..住? Why do we say 我住在..？
Generally speaking, the two structures


我在ＬＶ
我Ｖ在Ｌ


where「Ｌ」is a location and「Ｖ」is a verb done at「Ｌ」are used for different purposes.

我Ｖ在Ｌ is normally used for stative verbs, that is, verbs which describe a state of being rather than an action. For example:


我藏在冰箱裏 (I'm hiding in the fridge)
我站在椅子上 (I'm standing on the chair)
我坐在沙發上 (I'm sitting on the couch)
我躺在牀上 (I'm lying in bed)
我活在世界上 (I'm living in this world)


我在ＬＶ can be used for other kinds of verbs, including stative verbs, so 我住在北京 and 我在北京住 are both acceptable.


  Dynamic verbs are not normally of the structure 我Ｖ在Ｌ, so e.g. expressing I'm eating at home as 我吃飯在家裏 is non-standard.