Probably the closest thing Islamabad has to a tourist district is the village of Saidpur. Nestled between two ridges of the Margalla hills right next to Islamabad is Saidpur village. It's hard to say exactly where this village begins and where Islamabad ends, but once you're there the feel of the city disappears completely. Saidpur is an example of what the capital region looked like before the capital city was built on this spot.
The front part of Saidpur is the more touristy area and the back is where the locals actually live. For the most part there's nothing to really see in the back portion of the village unless you happen to be using Saidpur as the starting point for a hike up the Margalla Hills. There is a trail that goes up the hill from the village, and it should be noted for security reasons, that the hike up the hill is the only alternative exit from the village from the main road.
The front part of the village is mainly full of restaurants, and frankly they're all very good. There is also an old Hindu shrine in the village that has been turned into a gallery/museum. Closer to the entrance gate you'll find an art gallery as well as a few cafes. Daytime is a fine time to visit, however at night is when this village comes alive. You may find that parking can be very tight since this is a very popular area to be at night, but there will always be someone to help you find a parking spot.