The only place I've eaten in Vicenza (for dinner) was Lo Scudo di Francia. It was recommended by a local, and the evening I was there, Count Valmarana (whom I had met when visiting Villa Valmarana ai Nani) was dining there with friends. It's not a quick and casual place, but it's very central to the main sights and, as far as I can recall, reasonable in price.
Here are three places in the centro from the soon to be killed Chowhound database. the first is dinner only, however. Hope you report back on your visit. vicenza is an interesting town.
0444 547897 - contra' Pedemuro San Biagio, 90, Vicenza, Veneto 36100, IT
open for dinner only, Slowfood
0444 323721 - Contrà Santo Stefano, 3, Vicenza, Veneto 36100, IT
closed Mon at lunch and Sun, recc by Plotkin and MIchelin
Antica Osteria al Bersagiere
0444 323507 - Contra Pescheria 11, Vicenza, 36100, IT
slowfood, open lunch and dinner, closed Sunday