Al-balad (old town)
Naseef House
The former house of one of Jeddah's main trading families is now being renovated as a museum of sorts. Great views from the top floors when it's open.
Jeddah's top sight is al-Balad, or the old town. The city wall has long since been torn down, but the old gates still mark where it once stood. Within you'll find a warren of ancient buildings and traditional souqs markets, and the teetering, multistory coral houses that Jeddah is famous for. Unfortunately, coral is not a very durable building material, and most of the buildings are in disrepair. Spend time wandering around the old city and get lost in the seemingly endless souks. You will find yourself in another world and entirely 'in' the world, surrounded by people form all over the arab world, Asia and Africa.
other
The Jeddah Corniche offers spectacular views of the Red Sea. Check out the main shopping street on Tahliya for interesting wares, and if you're looking for good quality gold, try the Gold Souq where you can bargain for 18k and 24k gold by weight. The King Fahd Fountain is not only the tallest water fountain in Jeddah, but also the world.