The town of Vicenza is a very safe place. I am regularly visitings this place and never ever have seen anything that might be considered as warning or danger. You can walk around until late of the night and feeling very comfortable.
The only "problem" you may have, visiting it out of the summer season, is in fact that most of the restaurant close at 10 PM. After that hour, speaking of week time from Monday to FridaY, the town looks like an deserted place.
A good and detailed map of Vicenza is absolutely a must while visiting the town.
Some of the palaces have the name displayed on the corner but most of them are missing and, as the buildings are so close one to each other, is easy to miss them.
Even if you have the number of the palace on the street is hard to find it as most of them, especially on Corso Palladio, are used for commercial reasons today and the number is not exhibited.
On Contra Porti is the most difficult to identify the building because there is no number or name around.
BE aware the the exit on the east (SR 11) makes finding your way to the old part of the city more difficult that the west exit SR 46). There are many connecting roads right at the exit, and with traffic flow, or in darkness of night, the signs and directions are hard to find. There is a perimeter road that runs parallel to the autostrada, and has signs to Schio & Thiene. That is the road to take to then get to the inner perimeter road, where the citta vecchia is located.
There are gypsy camps in and around Vicenza. Normally there aren't any problems with them, except for house break-ins, but I wouldn't go wandering around inside one of the camps if I were you.
This one is on Viale Cricoli near Bassano Circle.
I was taking pictures of the ducks and swans and noticed two swans submerge and then start swimming toward this poor duck that was just floating there minding his own business - he even seems to have a smile on his face. Then the swans emerge right under the duck and scare the daylights out of him.
As you can see, I caught the practical joke on film