Stayed in the IC recently on Sweet Dilemma nights and had a fantastic stay. Nice leisure facilities + got upgraded to the very nice Executive Club which overlooks the Bosporus. They provided not just breakfast but a substantial supper (accompanied by alcoholic drinks) and afternoon tea so we didn't buy any food at all during our stay.

The IC isn't actually that far from the Old Town - maybe a couple of miles. We travelled to it in 3 different ways, all worthwhile:
1) Walked directly down a very pleasant and interesting street (Istiklal Caddesi) with lots of shops, restaurants etc on or near + an Orthodox church. Took about 40-60 minutes at a brisk but leisurely pace.
2) Walked downhill, again through an interesting area, for about 10 minutes and pick up the tram to the Old Town.
3) Walked slightly more indirectly by starting down Istiklal Cadessi then dropping down to the Bosporus through very trendy and arty Cehangir (more nice cafes, restaurants etc) to the road by the Bosporus, then walked along the tram route. This is a bit of a busy road but we found it interesting as it goes past the cruise ships and the new Istanbul Modern complex.

You wouldn't want to walk back at night (not dangerous, it seemed a very safe city - but you might find it hard to navigate in a couple of places) but, if you're mobile, I would definitely recommend walking in.

Another big advantage of the IC is that it is only a couple of minutes from the airport bus (run by Havas) terminus.

Take all these together and I would go for the IC every time - indeed I'm already planning my next trip.

If it's your first time in Turkey note that you have to queue three times at the airport - first to buy your visa, then passport, and then customs. When we we there there some very angry Americans who'd queued an hour for passport only to be turned back because they hadn't brought their visa first.