I would suggest the Taksim or Sultanahmet areas of Istanbul would give you the best central locations for exploring. Istanbul has lots of historical sites - split between the Asian and European sides, so be prepared to do a lot of walking etc, although the metro and the water taxis are good ways to get round.
One weekend is a very short time in Istanbul but I would recommend the following places:
Sultan Ahmet Mosque
Underground cisterns which are amazing
Boat ride on the Bosphorous
and if you are feeling brave, then a trip to the bazaar is a must
There are lots of good restaurants, bars and places to sit and watch the world go by. about 7 years ago