I've just spent a month in Curitiba and I greatly enjoyed the city It's a very charming place, resembling a huge residential area for families. It's also a very clean and peaceful city, and I felt safe there (unlike in particular areas of certain other cities in Brazil).
If you happen to be passing through the South, Curitiba could make for an interesting stop on your itinerary. However, it has neither beaches nor historic monuments, in fact no specific monuments or interesting places to visit at all. It's not worth making a trip to Curitiba when traveling Brazil unless the city happens to be on your itinerary. Don't go out of your way to see it.
I wouldn't go so far as to say that Curitiba is an essential place to visit when visiting Brazil. Tourists, in fact, quite rarely include it in their circuit. It is, nevertheless, an interesting destination, and one that can be visited quite quickly (one whole day) as a stop off on the way to Foz do Iguaçu, for example.
Curitiba's big attraction is its large number of green spaces. In particular, go for a stroll around the paths of the botanical garden. The greenhouses there are one of the city's most famous places. You can also go for a walk around the city's historical center, where several of the streets have been pedestrianized. The thing that made the greatest impression on me when I was in Curitiba was visiting the Niewmeyer Museum, which is also referred to as the Eye due to its shape. Apart from the architectural interest of the building itself, the museum also puts on temporary exhibitions. The one about Brazilian design that was being held when I visited was of very high quality.
Curitiba also serves as the departure point for a quite incredible train excursion, which goes to Morretes. Over the course of the three-hour journey, you pass through areas of protected mountainside forest: the Mata Atlantica. Whether it's fine or overcast, the scenery is absolutely stunning.