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Vyšehrad,
A casual walk (or tram, and reverse the process) down the river takes you to this excellent fortification. Normally well away from the crowds, and certainly worth exploring. Here, from one corner of the walls, you can see right across the river to the castle complex that most people visit.
At the 'Ghelná Gate', there is a small tour that takes you under the walls, into what is now one single chamber, though it was on two levels once. In here are the original statues from Charles Bridge. All very weird and gloomy.
We also have the church of Peter & Paul, plus cemetery where many famous people of the country are buried.
According to ancient legend, this was the first seat of Czech royalty. It is certain a castle has been here from at least the 10th century.
If you can find time to fit a small boat trip in whilst visiting the city, you get stunning views upwards from the river.
And if you walk back you can make a day of it by visiting the nearby botanical gardens.
Oh!
And there is an excellent little bar/cafe on the site, so you will not go hungry or thirsty.