Rapperswil has a wonderfully preserved old town. Most houses go back to medieval times, details from that era like portals, reveals and such are still to see, while facades were reconstructed in recent centuries. It's fun to walk along cobbled, narrow alleys (see off the beaten path tip for Hintergasse), do some window shopping, drop into a little cafe or shop, watch the other people ...
Sooner or later you'll pass Hauptmarkt, the main square with a fountain and several cafes/restaurants, where a flight of steps leads up to the castle hill and catholic parish church, and you'll end up at the beautiful lake promenade with even more cafes and restaurants.
Favorite thing: The Tourist Information Rapperswil is located at the square "Fischmarktplatz" on the ground floor of the car park "am See". The competent team will answers all your questions about your travels. This tourist center was awarded for the mark of quality of Swiss tourism.