The Veneto Region is perhaps one of the best regions in Italy to explore by foot, regardless of how you get here and plan to spend your time you need to bring a good pair of walking shoes. The cities of the Veneto are compact and best explored by foot. Example being Venice (Venezia), Venice Province, if you only ride around the city using the waterbus you stand the change being disappointed and never grasping the wonder of the city. The main transportation only gets you to some of the principle sights but to truly explore the city you need to wander the alleyways and get out on the small islands of the lagoon. As well, Vicenza and Verona, are two main cities not to miss, and you will need to walk most of the day, if you want to explore.
With multiple walled cities dating back to the 1100's; Cittadella, Castelfranco, Marostica, Soave, and several others, using the train and systems you can enjoy a very enjoyable vacation of exploring. Keep in mind many of these small towns are located near the wine producing zones, so an additional shuttle on a urban bus can get you out into the 'countryside' where you can wonder secondary roads and trails.
If you want to explore a bit further afoot you have the hills of the Berici south of Vicenza with many hidden gems to discover, the volcanic hills of the Eugenia near Padova, the hills of Asolo and the Prosecco wine area, or the hills over near Verona and the southern shores of Lake Garda. Each of these areas has a unique history and special flavor. And many are located close enough to the mountains of the PreAlps and Piccolo Dolomites to offer special excursions like the battlefields of WWI, Asiago Cheese area, the unique eco-system found on Monte Baldo above Lake Grada.
Fo those that are looking for great multi day pack treks then the Dolomites has multiple trail systems to follow for classic treks, or grab a few maps and design your own walk. The Veneto Dolomites are all in the Belluno Province,and most are part of the UNESCO World Heritage Site.
Grab you walking sticks and let's go!!