Well, attractions or recommendations below are maybe not that unusual for a typical Czech citizen but they might be for tourists.
Where: Rašín´s riverbank, near Palacký´s Bridge. Tram stations: Palackého náměstí, trams 3,7,10,16,17 or Výtoň, trams 3,7,17. Metro station: Karlovo náměstí, exit: Palackého náměstí
+ Markets every Saturday 8-14
It is a riverbank, Rašín´s riverbank to be more specific. 4 years ago this place was just a boring Prague riverside with nothing but swans and pigeons. Today, it is a vigorous and inspiring place, especially during summer. People gather there to drink and to enjoy beautiful view and various events: concerts, farmer´s markets, dancing performances...It is a nice place to go in summer when you do not want to stay inside in pubs or clubs. It is healthy as well since you can walk along the river for many hours. :D
Divoká Šárka - Wild Šárka
What: A large park on the northwestern outskirts of Prague. Tram station: Divoká Šárka, trams 8, 26 - they go for example from metro station Dejvická or Nádraží Veleslavín.
Ok it is not only a park but a wild natural reserve, a perfect place for a day out. There are many possible routes to
choose from so one visit is simply not enough. It is named after Šárka who was a beautiful warrior in a ladies-only group (something like Amazons) during the Maiden´s Wars. It is said that once this group controlled the city and they were in a constant fight with a rebelious group of men. Šárka set up a trap for Ctirad, a leader of the opposite group, and with this help Ctirad and his comrades were killed by Šárka´s fellow fighters. According to this myth, Šárka was remorseful and threw herself off the cliffs in this park - this specific place is called Girl´s Jump (Dívčí skok).
You can start your walk at Divoká Šárka tram station, the road down into the valley starts behind McDonald so it is not that hard to find it. During summer you can visit the local swimming pool that offers other sport activities as well. There is also a reservoire called Džbán with occasional concerts.
SAPA - Vietnamese shopping and cultural centre
Bus station: Sídliště Písnice, buses 113, 197, 331, 333 - they go from metro station Kačerov (C)
The Czech Republic is still pretty much homogeneous in terms of other minorities living within the country. Inhabitants of Vietnamese origin are one of the largest groups here and SAPA is their cultural centre and also a marketplace. It is not far from the city centre and it can be a different Prague experience. There are many possibilities to try Vietnamese cuisine as well. Buddhist temple is in the areal also. You can visit the place individually or make use of the tours that they provide in SAPA: http://www.informace-sapa.cz/index.php/cenik-prohlidky-a-sluzby - 190 CZK/person for a normal tour, food tour 190 CZK/person and shopping tour 250 CZK/person.