Take a cruise upriver: Go at least as far as Pinhão - the landscape is absolutely stunning. If you choose to do this in the summer, don't forget your factor 50 sun screen! Cruises on the Douro River.
Go on a self-guided walking tour of the city of Porto.
You might also want to visit the Dragão Stadium, home of FC Porto. The team has a rich history, having won the World Club Championship or Intercontinental Cup twice, Champions League twice, UEFA Cup once and UEFA Supercup once - and the stadium is worth a visit on the architecture alone. If you are lucky you might get to see a game of the Champions League... also, just across from the stadium you have a large shopping center, according to a joke built to block the wind from affecting the stadium.
I would absolutely suggest taking a port wine tour! This is a must as Porto is the port wine capital (or so they've self-proclaimed) but the value is phenomenal. The cellars are in Gaia, across the river, and there are extremely convenient bus pick-ups from easily accessible areas to take you up the winding hills to the cellars. I couldn't believe the price: I paid 3 Euros for a tour that lasted approximately an hour, with a tasting. I believe most all have English speaking tours and my cellar had English, Spanish, and Portuguese. I wish I had had time to do them all! There are quite a number of free tastings where you will get a couple of glasses.