Greg, glad you've decided you can do Istanbul on your own--it's a wonderful city and nice to have the freedom that second day. Depending on whether you take a tour the first day, and what tourist sights you might already have covered, there's the main tram that wends its way through the city from somewhere close to the cruise port across the Golden Horn to the historic area where man sites are grouped close together.

There's also a Hoho bus which makes a large loop and gets you to a bunch of interesting sights--we took the Hoho over across the Galata bridge, got off at Taksim, walked sharply *downhill* on Istiklal Caddese, which is a very interesting shopping street, picked up the next stop and continued on our loop over to the Chora Museum (medieval mosaics, amazing). I think you can also get close to the Suleymaniya mosque, which is a spectacular sight as well, and not crowded with tourists (it's close the Spice Market as well.)