When you think about it, most tourists to Bahrain have no idea where to go to see historic sights and so on. Most of the history has been wiped out to make way for new roads, business centers and shopping malls, but whatever history is left isn't really promoted well; when a tourist asks where to go, they're usually guided to Seef Mall, Bahrain International Circuit, and a bunch of other modern creations that really don't show any of our past, which is actually very rich with culture and history. I'll cover most of the sites you should take a look at if you visit:
Arad Fort is a 15th century fort (exact date of construction is not known) built by the Portugese. It is located in Muharraq, very close to the airport, so it is probably the first sight you will see on your visit to Bahrain.
The fort isn't very big, but it's definately something to see. Make sure you wear a good pair of shoes (no high heels!) especially if you're planning on walking up the stairs, and take a camera along!
But the visit isn't free; entrance is a whopping 200 fils (approx US Dollars $0.52), so make sure you pass by the bank before visiting!