Elizabeth said:
Isn't it acceptable as well not to use いる or 滞在 at all, or to tack on も （週間も) as a way of emphasizing the amount of time.
週間（も）アメリカに行く（つもり、よてい）です、 I will go to America for a week.
First, you need to have it 一週間, not 週間. And then you would only want to use the も to emphasize the amount of time if there was really some reason for emphasizing the time....as in "Wow! A whole damned week!", in such case as where a shorter visit would seem the norm, you see.
Constructed the way you have it, the 週間 modifies the act of going itself, not the fact of being there. Compare:
一週間（も）勉強するつもりです。
The action continues throughout the week, and the time expression has nothing to do with what comes
after that period.
一月くらいやり続ける。
Same as above. The action continues throughout the period indicated. Furthermore, it implies that the action will cease at the end of the period, so we can see that the time expression has no relation to the action following its end.
So if we're going to indicate a period of stay, we're going to need to have a verb that's indicative of the action/state that exists after the going, if we must indicate the going.
Fortunately, if context lets all parties involved know that the speaker is not currently in Tokyo, but will be going, then there is no need whatsoever to indicate the going action in the Japanese sentence. It's redundant, and the only reason we so desperately feel the need to cram it in there somewhere is because we have the "I'm going..." thing in the English counterpart. By saying 東京に一週間いる we have conveyed all the essential information (the location and the period of the stay). If context makes it clear that the destination is Tokyo, we can leave that part out and just make it 一週間いる.
And thanks to whoever gave me the rep points for my uncharacteristic participation in a language thread.