The Hotel Agan is good, as is the Zeynap Sultan both small & friendly hotels in SultanAhmet just a couple of minutes walk from Hagia Sofia, Blue Mosque etc. This is definitely the best area to stay if you want to be within walking distance of some of the main sights (including Topkapi Palace, Basilica Cistern, Galata Bridge etc) & close to the tram links. The last time we stayed at the Agan (January 2012) we got the best price through budgetplaces.com
If you are flying into Ataturk airport the taxi fare (metered) is 40TL into the city & takes about 20 minutes, which works out about the same cost as using the hotels' transfer services which are usually shared shuttles (but not always).
Enjoy your holiday!