The cathedral st. Urs and Victor and its tower which can you can go up.
The clock tower and the rest of the old town.
Einsiedelei im Verenaschlucht Hermitage in the Verena gorge (http://www.solothurn-city...), which you can reach in a 45-minute walk north of the city. It's located in a forest and is a beautiful place to walk around, especially in the evenings when candles are lit and placed in between the rocks throughout. Look for signposts and ask around. Please don't abuse this off-the-beaten-path gem and keep it quiet and peaceful as it is a path of meditation.