Next week, in the next week, for the next week
1) At some point during the next week, you will probably go to the mountains, but you do not intend to stay there for the entire week.
"at a specific moment in the next week"
2) You intend to go on holiday for the entire duration of the the next week.
"for the entire duration of the next week"
3) During the course of the next week, you expect a lot of work.
"during the course of the next week"