Porto has good food, but Francesinha should be on your bucket list. It is a really heavy dish, so split with a friend. I am not sure which place had the best one, but I guess just ask the locals. Rest, here:
Casa Guedes - pork sandwich. https://goo.gl/maps/LeQJzT8XCx32
Majestic Café - fancy cafe, over priced, but worth a peek. https://goo.gl/maps/u2pbLGf37bH2
Restaurante Conga - popular for beefanas, pork sandwiches. https://goo.gl/maps/yRzFPo4Qsj32
Novo Mondo - local food, potatoes etc. https://goo.gl/maps/8hsKAGomVru
Adega Vila Meã - old school Portuguese place. Local food. https://goo.gl/maps/c6mMrPhnMpM2
Flor de Bragança - local Portuguese place. https://goo.gl/maps/RJZ1CaDcCWQ2
Base Porto - outdoor bar in city center. https://goo.gl/maps/JjenK8RA7JJ2
Taberna Santo António - local food, very good food. Try to reserve if you go. https://goo.gl/maps/EPaZ6EYDiyo
Apart from these, you can go to Matosinhos, a suburb or Porto where the beach is. There are several fish and sea food restaurant. Pick any, it's hard to go wrong. There is a long beach here. Walk from Matosinhos to Foz do Duoro.
You can either watch the sunset from the botanical gardens or be a bit adventurous and climb the bridge Arch and watch it from there:
Harbor Bridge Climb https://goo.gl/maps/NBF1roYwK1C2
I would really recommend you book the sunset climb. Its short and easy, but the view and feeling is unique.
You should definitely go to the other side of the main bridge, i.e. Gaia. There you get a nice view of Porto, and also get to taste a lot of port wine.
If you have couple of days extra, you can take a wine tour on the Duoro, or go to Guimaraes, the town where Portugal was born. If you are really into wine, you can also spend some time in the wine region nearby. There is a nice train ride on the hills, alongside the Duoro river, which will take you to small wine growing villages.