Akbiyik Degirmeni Sk no:46
That is the view from one of the two small rooftop terraces. It’s taken with a zoom but yes, this budget hotel is really that close to the Blue Mosque in Istanbul’s Sultanahmet district. Pretty nice, no?
The rooms were a bit small but comfortable, there’s free wifi throughout, and the breakfast (included) was quite good, a blend of western and local, with the emphasis on the local. All that, plus a very hospitable and welcoming staff, for 35 EUR/46 USD/night (I booked through venere.com).
What’s most appealing is the location, set on a quiet mostly residential street but less than a 10 minute walk from the Blue Mosque. Both the Grand Bazaar and the Spice Market/Eminonu Square were a leisurely 20 minute stroll away. Nearest tram stop is Sultanahmet (2 TL per ride), roughly midway between the Blue Mosque and Hagia Sophia, is also a 10 minute walk. There are plenty of cafes and restaurants just a short walk away as well.
It’s a bit difficult to find initially, so be sure you give your cab driver the exact address. Taxi ride to the airport (40 TL/16.50 EUR/22 USD) took just over 20 minutes in mid-morning but you should probably give yourself twice that.
Oh almost forgot: the wall surrounding the courtyard is 1600 years old.
(I stayed at the Sphendon for three nights, 12-15 March 2012).