I think 'sitting' means the same in the biblical passage as it does now, in our day.
See example at: http://www.businessinsider.com/stocks-gop-congress-sitting-democrat-president-2014-11
The terms used are 'sitting President" and mean one who is 'in office' and 'on the job', engaging in the tasks of their position.
κάθημαι kathēmai- is the root , translated here and elsewhere as 'place', and 'dwell', so with these meanings we can put together - "the Harlot's place where she dwells and engages in activity from."