I've been to Lisbon a couple of times and enjoyed both visits. There's a lot see in the city that I once saw described as looking more like the Americas than Europe. I thought that was a fair comment with the huge suspension bridge spanning the Tagus river, the statue of Christ looking down at the city and the steep hills and trams that are all reminiscent of famous places in the New World.
But this is a European city steeped in history, the most westerly city on the mainland of Europe in fact. The old town incorporates the Alfama district, one of the oldest in the city where Fado music can be heard in the bars and cafes, the 12th century cathedral resides and the steep narrow streets where the famous tram number 28 trundles by (see picture) not forgetting the 11th century castle that sits at the top of the hill and where the views of the city are spectacular. The old town is largely in the upper area and there are a couple of novel ways to get there, funicular Gloria is one way and the Elevador Santa Justa (Santa Justa lift) is another and once at the top you can ascend some steps to a viewing platform for an amazing view of the lower city.
Much of the lower city was destroyed in 1755 when an earthquake devastated the area. The lower area today has wonderful large squares, an impressive railway station, the Rosario, built in the Neo Manueline style and all the shops and amenities you expect from a capital city.
For Manueline Gothic head to the suburb of Belem and visit the Jeronimos Monastery and possibly the most famous of Lisbon's sights, The Tower of Belem standing in the Tagus river.
It's also worth mentioning the impressive monument to Henry the Navigator, also in Belem and the really excellent, free to visit, botanical gardens in the north of the city. If parks and gardens are your thing Lisbon doesn't disappoint, they have a large selection.
It's also possible to visit the Lisbon Aquarium which was well worth the short tube ride and then take the cable car over the old Expo area with views of the city.
It's fair to say that Lisbon has something for everyone and it's a great but possibly often overlooked city break destination.