Here's a few tips by BeautyofPrague.com:
Vysehrad, Petrin and Jewish Town
If you do not want to miss iconic views of Prague Castle and its surroundings, you should definitely not miss Petrin or Vysehrad. Just Vyšehrad will surprise you not only with its mysticism, which is not only the legend and the famous cemetery. You will also be delighted by the fact that the distance from the center eliminates the number of tourists to a minimum, there you will be able to enjoy the beauty of the Basilica of St. Peter and Paul or the Rotunda of St. Martin.
You can also visit the Jewish Quarter for history. Although Josefov changed considerably during the renovation of the 1880s, several buildings that still hinder you from the past. For example, you can visit the Old-New Synagogue all year round with the exception of Saturdays and other Jewish holidays.
You can also go to Strahov because the local monastery hides a unique library that will undoubtedly attract you not only with its rare collections. The Church of St. Nicholas in the Lesser Quarter, whose tower offers really unusual views of both Charles Bridge and the Castle, is also unjustly neglected. On the way from Mala Strana, you should definitely not miss the narrowest street of Prague, which is controlled by a traffic light.