Ideally it should be one that can be expanded to a full month view if necessary and back again.
Also, (css based?) design customizability would be a plus.
A jQuery solution would be preferred. I've had a brief look at the jQuery datepicker, but it seemed to me that it can only display full months. Please let me know if I am wrong.
The jQuery UI datepicker, as has been noted, can not easily be configured to display only one week. You can however use the
minDate configuration options to constrain the user's input. Here is an example of this functionality.
To answer your specific question, I am not aware of any datepicker control which will only display one week.