A city built on seven hills, Istanbul is divided from north to south by the Bosphorus ( a strait that connects the Black Sea and the Marmara) into the European and Asian portions. The European portion is further divided by the Golden Horn (a freshwater estuary / a really short river) into the Old City and Beyoglu.
The Old City is the area that includes Sultanahmet and the Grand Bazaar, basically all the touristy spots.
As I discovered from the Lonely planet guide, Beyoglu is the Turkish name for the two ancient cities of Pera and Galata. Beyoglu includes areas like Taksim square, the five star hotels like the Hilton, Hyatt, The Marmara etc.\, and, as per tourist guides, the heart of Istanbul!
When I asked the hotel reception, I was informed that all the touristy stuff is on the European side. The only tourist attraction / place of note on the Asian side is the Haydarpasa Station which is the railway station for all trains going to Anatolian region. Since we were only going to be in Istanbul decided to give it a miss. I would much rather see the station near Eminonu, which is the station where the famous Orient Express used to arrive!