All the places already mentioned would certainly make excellent day trips. In addition, some smaller places just to the north of Padua and Vicenza seem very interesting, although I have rarely seen them mentioned on this forum and they do not seem to appear in RS books. These include Cittadella, Castelfranco and Bassano di Grappa. I will be in Verona, also in late May, and hope to visit some or all of these three. A little farther north is Cortina, which has been recommended to me. Finally, i don't know what causes you to be in Padua for nine days, but depending on your interests, there are various interesting visits in Padua itself. Among these, Giotto's Scrovegni Chapel requires advance reservations. Also, the central market in Padua, both inside and outside, is one of the most famous in Italy.