Basically '-ni' indicates the place of existence, or destination. '-de' indicates the place of action.
A) chikoku dewa surukoto ga takusan arimasu. (I have many things to do in chikoku)
B) chikoku niwa surukoto ga takusan arimasu. (There are many things to do in chikoku)
Because the verb 'suru' is an action, 'chikoku de suru' is a natural connection.
And because the verb 'arimasu' is a static, 'chikoku ni arimaru' is natural.
So, A is an explanation of somebody's schedule. You will be busy in chikoku.
And B is an explanation of the place 'chikoku'. chikoku has many attractions.
C) chikoku niwa isshukan imasu.
D) chikoku dewa isshukan imasu.
If you say 'chikoku de imasu', I would not accept it because 'imasu' is not an action.
But 'chikoku dewa isshukan imasu' is a possible expression though it seems a little bit strange.
Because of the word isshukan(one week), we can imagine that the word 'imasu' is not just 'stay' but there would be many activities. So we can't reject this expression simply because the verb 'imasu' is a static verb.