Formal:
* See you next week. (most common)
* I'll see you next week.
* We'll see each other next week.
Informal:
* Catch you next week.
* See ya next week.
Specific to a situation:
* I'll see you next week at the meeting.
* I'll see you next week for our appointment.
The key to finding the right translation is to understand the context and the relationship between the speaker and listener.