We have a layover in Istanbul in a few weeks time so looking for some advice on what to do. Arriving (from OSL) a Saturday at 17:15 and departing (to BKK) "the next day" at 00:40. Unfortunately this is too late for the free Turkish Airlines tours mentioned above.

Also, a lot of the typical tourist sites will be closed or closing at that time, e.g.
Hagia Sophia Tu-Su 9AM-6PM
Topkapı Palace M,W-Su 9AM-5PM
Sultanahmet Mosque (Blue Mosque) Nov-Apr:9AM-7PM (we might attempt this)

Similarly, it appears that cruises are more common earlier in the day (and might require some more time).

There is a free organized walking tour which starts at 18:00 which we will try to join (realistically though we will be too late for that as well).

At the moment I am leaning towards strolling around, visiting a hamam and perhaps getting dinner. Any other suggestions are most welcome.

I have also heard that the TK lounge is quite nice and would like to check it out. Some people report long lines at check-in/passport control; is this likely to be a problem on a Saturday evening? Also, there is apparently direct access to the lounge (and a separate passport control). Is this easy to find?

Finally, would the quickest option to get into town be a taxi at that time?