Istanbul subway map or to copy it for yourself click here : http://www.istanbul-ulasim.com.tr/harita/IstanbulHarita.jpg
Sultanahmet Area is the most common area in Istanbul. There are many main historical places, hotels, hostels and others ...... I think many of guests stay at hotels or hostels near to Sultanahmet. But if you stay somewhere far the easiest way to reach there is to take Tramvay line Zeytinburnu - Kabatash and go out in stop named Sultanahmet. My suggestion for someone who will visit Istanbul first time is to spend first entire day there . In my opinion first place that you should visit is BLUE MOSQUE. Why do i advise you to visit it first ? Cause in the afternoon time there is pray time and it might be closed vor visitors for a one hour. Thats why visit it in the morning :) .
The enter to Blue Mosque is free. Second place should be HAGIA SOFIA . The enter there is 20 turkish lira about 10 eur for tourists for locals as well. A few weeks ago i have watched on National Geographic realy interesting documentary about building of H.S. It was built by two architects Antenius and Isidor. Rome Imperator Justinian gave them 5 years to built the biggest church in the world. It took four years to built only cupola. And in the one year they finished all. Third place should be BASILICA CISTERNS http://en.wikipedia.org/wiki/Basilica_Cistern
. Then maybe have an easy lunch somewhere in nearest not expensive restourants. and after continiue exploring magical places :). Fourth place should be TOPKAPI PALACE . It will take maksimum 3 hours to explore the palace. After i advice to walk to Eminonu area thats in close to Sultanahmet area to see EGYPT BAZAR, YENICAMI MOSQUE and GALATA BRIDGE. For one day it will be enough to see and be impressed . In order not be tired i advice you to finish your day there and after resting you can go to watch DERVISH SHOW ( SEMAZEN SHOW ) somewhere in Sultanahmet .