Pirna's greatest value as a base is the Saxon Switzerland national park on its doorstep. The three most rewarding targets are Bastei, Königstein, and Bad Schandau — each a distinct experience, each reachable in under an hour.
Bastei is the most famous, with its sandstone towers rising above the Elbe and a 19th-century stone bridge threading between the rock pillars. It's very popular in summer; arrive early or late to avoid the worst of the crowds. The views over the river valley are among the best in Germany.
Königstein Fortress sits on a flat-topped sandstone mesa above the Elbe, about 30km from Pirna. It was never taken by force — a claim very few European fortresses can make — and spent centuries as a treasury, a state prison, and a refuge for the Dresden royal court during times of war. It is a half-day at minimum.
Bad Schandau is the hub of the national park, with good hiking access into the Kirnitzschtal valley and the Schrammsteine rock formations. The town itself has a pretty riverside character and is the starting point for several of the best walking routes in the park.
All three are reachable by S-Bahn or bus from Pirna, or by the paddle-steamers on the Elbe in summer.