An experience not to be missed is taking one of the budget ferries out of Riva del Garda to one of the medieval lakeside towns.
The ferries are fast, efficient, and on time. The slowest ferries offered by the ferry service Navigazione Lago di Garda are cheap and leave you the most amount of time to admire the stunning mountain and lake scenery. The Navigazione Lago di Garda also offers hydrofoils, which are much less adapted to sightseeing (as you are forced to sit below deck in an enclosed space) but do have the advantage of getting you to your destination quicker.
From Riva's main square, walk towards Hotel Europa and watch for the metallic silver booths where tickets are sold for all ferry trips. Tickets should be bought from Navigazione Lago di Garda before boarding - and don't listen to touts suggesting otherwise.
The shortest trip out of Riva (and one of the most beautiful in terms of scenery and destination) is to Limone. Limone is a medieval town with cobbled alleyways, made famous for its ancient lemon groves (limone in Italian). The best place to see these old wooden groves is from the ferry as you dock into Limone's very Mediterranean-looking port. A happy afternoon can be spent wandering around Limone looking at trinkets and climbing up to the church above the town.
Other possibilities by ferry: Malcesine, painted by Klimt in a now lost picture, with its medieval castle, or Sirmione, right at the other end of the lake. Sirmione is well worth a long day trip to visit the Roman ruins and healing mud baths.