Actually, Kadikoy which has easy access to SAW, on the Asian side of Istanbul is a great place to stay during your visit to Istanbul ( I stayed there for 35 days with airbnb) But the consensus on this board is NOT to recommend the Asian side for first time visitors. Which I kinda understand that argument and kinda agree with.

If you're arriving in the main Ataturk airport use the metro outside the airport to get to Zeytinburnu then switch to a tram for Sultanahmet where there are many pensions, hostels, and hotels. http://www.tripadvisor.com/ShowTopic-g293974-i368-k6648758-Ataturk_to_Sultanahmet_via_metro_tram-Istanbul.html
"5. From Zeytinburnu metro stop, walk south toward D-100 Yanyolu to Zeytinburnu tram T1 stop. Google Maps says the walk is 50 meters and 1 minute.
- Take tram T1 toward Eminonu. Get off at Sultanahmet (the 16th stop)."
You will need 3 -4 lira for tokens for each section.
I note you say you arrive late at night so public transport is likely out for you but it seems a pity to pay out for an expensive transfer.Why not book a shared shuttle transfer?This is door to door service ,payable only at the door of your hotel and is only 10€.Safe and cheap :)This company operates from both airports-
http://www.istanbulairportshuttle.com/
With this you can stay anywhere you prefer rather than be dictated by hotels.How long will you stay?If only for a few days then Sultanahmet/Gülhane or Sirkeci puts you in the heart of the ancient city.Or Beyoğlu,Galata,Cihangir in the more modern nightlife area.Give me a rough idea of budget and I'll give you some suitable suggestions.
On Fridays everything is open as normal.The only chnage is that touristic mosques like BLue Mosque are closed to vsitors until c.14.30 but they stay open later that to compensate.
You're welcome :) One point I must make;I just learned a day or two ago that the shuttle is now 15€-probably due to the huge dive TL is taking right now.Still good value though and safe.

I can recommend 'Noble House Hotel' just 3 mins from the Galeta Tower. Each room is decorated differently and it has a private terrace. If you book for 5 nights you receive a free airport pick up. Ataturk is about 14 Klms away. Breakfast is included and is delicious, the staff are very helpful and friendly.
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