As Adrian says, both sentences are potentially correct, but the meaning is different. Here are two scenarios:
1. I'm presuming that the person being addressed has been 'here' for only a short time, and that they're intending to remain here for several weeks, months or even longer. At the moment, this person doesn't find something entertaining, but the speaker is reassuring them that over the course of the coming week they will begin to change their mind. The speaker is referring to one week from now. Is that the situation? If so, then the first sentence is correct: "When you've been here another week, you'll find it quite entertaining."
In this scenario, the second sentence is wrong. You need to use a present perfect to refer to the length of time already spent in the place.
2. The second sentence would only be correct in the following scenario: 'Here' is a place where people spend a week, go home again, and then return on a later occasion to spend another week. Perhaps it's a holiday camp, or a health club, or a college that does one-week residential courses. In this situation, it would be correct to say, "When you are ( meaning 'When you return') for another week (meaning 'a second one-week visit'), you'll find it quite entertaining".
This is a less likely scenario, so I'm guessing that this is not what you are trying to say.