Do not be shy and enter the gate of the Strahov Premonstratensian Monastery which takes you to the courtyard. There you can enjoy nice interconnection of the creepers and buildings (I am going to post picture of it next time).

You can also find here the Strahov gallery, but as I am not art lover I have not been inside and I can not tell if it is worth a visit. But I am sure that the architecture of the Strahov Monastery is wort seeing also from the courtyard.