During Eid, Dhaka's streets empty out as people head home to their village for Eid. So it is a good time to explore Dhaka without the traffic madness.
I have a route that I often follow when friends and relatives ask me to take them on a tour of old Dhaka. This route takes 3-4 hours and covers several highlights. Note that you should call ahead to find the timing of gated places, such as Lalbagh or the Church.
Anyways... the route is described in my Tangents column today.
If you have a car, you can get dropped off in front of the Court and get picked up in front of Dhakeswari Temple at the end of your tour.