Kungsträdgården is the square/park that is considered by many to be the center of Stockholm, and chances are high that you will visit or pass through this square at some point during your visit to the city, especially as several of Stockholm's landmarks are located on or around the square. The name means "the king's garden" and was originally (as far back as the 1400's) a garden belonging to the royal family. It wasn't until the 1700's that the general public were allowed to visit the gardens.
The square also hosts several festivals through the year, like the Taste of Stockholm restaurant festival and Culture festival, as well as smaller events and concerts. During the winter months they open up a popular outdoor ice-skating rink in the square and most Stockholmers make a pilgrimage to the park in the springtime to see the cherry blossoms in bloom. Otherwise, this is a square where locals like to meet up with each other, spend a lunch break with colleagues or just take a stroll through on their way to do some shopping.
...cherry blossoms in the spring.
As I mentioned, the square is centrally located. To get there from the Hotel Rival, you can either take a 30 minute leisurely stroll through Gamla Stan (the old town), a 15 minute bus ride or take the subway. For the subway, you can just take it three stations to T-centralen, exit to Sergels torg, and walk two blocks or switch from the red line to blue line at T-Centralen and continue one station to Kungsträdgården. Of special note, this subway station is one of Stockholm's most beautiful and worth a visit on its own.