Considering this beverage is named after the country, it would be impossible to not encounter Port wine while in Portugal.
Porto, Porto, Oporto.... these are just some of the names for this nation's famous beverage.
Port is a fortified wine historically made in Portugal. In Europe, this beverage legally has to be made in the Douro River Valley in Portugal to be considered Port.
So, what is fortification again? Fortification is the process of taking a beverage and adding a distilled alcohol to it. Distilling wine is a fancy way of making it an even stronger drink. Port wine is usually around 20% alc by volume.
It is import to admire that in the 17th century, the Portuguese dedicated themselves to producing a wine with an above average alcohol content. Well done, Portugal.
A hilarious fact is that it is also believed that the discovery of fortified wine was an accident. The Portuguese enjoyed this strong accident so much that they started mass producing it. The terrain in the Douro River Valley lends itself to being able to produce grapes for this purpose, and it was highly demanded in Portugal's ally at the time, England.
Every restuarant will have a Port on the menu. The best way to know what to order is to ask your server for help. It is guaranteed that they know more about Port than you.
The city of Porto is the port capital of Portugal, so the beverage is omnipresent in the city. A tour of the Port houses is considered a "must do" for any visitor, and most people drag themselves up and down the hills of the south shore of the city to try Port after Port.
Here is the thing.... you really only need to visit one Port house to get the idea.
Port is an unique drink. If you were raised with it as part of your culture, I could understand gravitating towards it. For outsiders, it is harder to appreciate the drink.
The drink is centered around Porto because the Douro River exits the country into the Atlantic ocean at the city of Porto. Originally, wine runners navigated the dangerous waters of the Douro in boats with dozens of barrels of Port stacked on the deck. An impressive feat considering the Douro river is a destination for white water rafting.
The exit of the Douro river made made Porto the major port for the trade of this beverage. Portugal used it's Port wine to obtain goods from other countries.
So, yeah, as interesting as it is, Port wine can be an acquired taste. One taste of a white and one taste of a red will be sufficient for most.
Visit a port house, and then spend your time adventuring in other parts of the city (like biking up the atlantic cost).
I suggest visiting Taylor House for a Port tour because they have the best view of the city. It is a relatively similar experience at all the Port houses, so choose the one with the bonus view.
After the "official tasting" has passed, start ordering a "White Port and Tonic" while out. This version of the beverage skyrocketed to the top of my "favorite drinks" list, and it a great way to "when in Rome" without having to drink straight Port.
Last note: Worldwide decline in the demand for Port has caused wine producers in the country to focus on making other types wine as well. Be sure to ask your server or someone working in a wine shop to recommend a bottle.