The main tourist spot in Venice is in the area comprising St. Mark's Square up to the Rialto Bridge. Everything around this area is also as well very touristic.
For what may resemble more an off-the-beaten-path experience, take some time exploring areas highlighted in yellow and beyond... and preferably during winter months.
It is generally considered safe to explore around Venice. Pickpocketing is however frequent so be sure to closely watch your valuable belongings.