Verona is a wonderful city to walk around, to soak up the atmosphere, to grab a coffee and people watch, and to shop. Spend your first day getting the feel for the place. Head for the Piazza delle Erbe in the center of town and wander the market, admire the fountain, smell the herbs on the market stalls. For a real sense of the city layout, climb the Lamberti Tower.
When you've had enough coffee here, head through the arch Arco della Costa - if the whale bone falls on your head you are a just person. Don't worry, it didn't fall on anyone else either and it's been there for centuries.
Now you're in Piazza dei Signori, the heart of political toil and strife for centuries. Admire the buildings - mainly the work of the 14th century Lords of Verona, the Scaligeri family. Visit their nearby, rather spooky tombs, then head off across the river to the Castelvecchio, another impressive stronghold built by the Scaligeris. This is now a wonderful art gallery.