Day trips I have done from Prague on my many visits over the last 20+ years.
Plzen, Pardibuce, Melnik ,Karlsteijn , Krivlokat ,Beroun,Ceske Budojovice ,Karlova Vary, Turnov ,Hruba Skala ,Benesov, Kutna Hora, Tabor, Teplice, Mlada Boleslav ,Velke Popovice ,Hrusice,and Pribram .Also many places within the greater Prague area ,Chyne,Ricany, Kladno, Uneticky ,Prohunice as well as many of the outlying neighbourhoods of the city. some of these visits are by bus or train , some by friends who have kindly driven me there. I have left what to do in these places openended as I have no idea of your interests, if you are travelling alone or what forms of transport you will be using.
An Alternative base for a few days could be the lovely city of Brno.