You won’t need a car to see Verona, actually it will be a hassle to have given the traffic and parking restrictions in the city center. However being an Americanized Italian, I can’t imagine life without a car, so I always had one, even in Verona. However I stay in hotels outside the city center (outside the ZTL) then I drive to the parking lot here, outside the city center walls but only one minute walk from the Arena. If you intend to stay in Verona, with a car, do the same and find a hotel with parking outside the city center.
At lake Garda I like the north side also (Malcesine, Riva, Limone, etc.) mainly for the majestic mountains around. The south side is kind of flat and the mountain scenery not there, although the towns are nice. Sirmione is very quaint and pretty but super crowded in summer, and weekends always.
A car is useful to have at the lake because trains are only in Desenzano and Peschiera, on the south side, but buses are available. The lake is indeed the largest in Italy and very long, so it takes a long time by ferry from Desenzano or Peschiera all the way north to Riva. A reasonable short boat ride alternative is from Malcesine to Limone. It’s a very popular ride and there are both public ferries and private boat excursions operating there. The most gorgeous drive is along the west shore (also featured in James Bond’s Quantum of Solace). On the same shore is also the Strada della Forra, a breathtaking drive through the gorges. I think that road might still be closed due to a landslide, so check if it reopened before going up.
You can check all of the above on YouTube videos or Google videos and images.