Rosenheim sits at the intersection of several good day trip routes. The Chiemsee — Bavaria's largest lake, known as the "Bavarian Sea" — is 20 minutes east by train; boats cross from Prien am Chiemsee to Herreninsel, where King Ludwig II's unfinished copy of Versailles stands amid formal gardens. The castle interiors are extraordinary, and the lake itself is beautiful.
To the south, Kufstein across the Austrian border is 30 minutes by train: a small town with a formidable medieval fortress above the Inn gorge, worth an afternoon. The Inn Valley narrows dramatically south of Rosenheim, with steep forested hills on both sides.
Bad Reichenhall is 45 minutes east, with its own spa and saline baths and the Rupertus Therme; the town is quieter than Bad Gastein and less spectacular but comfortable and cheap. The Berchtesgaden valley — with the Königssee lake and the Eagle's Nest — is reachable from there by local bus.