The castle area in Prague is west of the river and can be reached easily from the east of the town by walking over the Charles Bridge. (Alternatively take the funicular railway to Petrin Hill and walk through the convent to the castle area.)

Mala Strana is the area at the foot of the castle and the steep streets lead up to its gates and entrance. At the time I visited the gardens were closed, check this before you travel if this is what you want to see. 

The castle area’s architecture is less ornate than the west side but interesting enough in its own right. Walk through the convent courtyard and you will reach Petrin Hill where there is an observation tower  and views over the city.