Basically, any place away from the Ferrovia/Rialto/San Marco pathways. But, a few specific suggestions on where to wander...
San Polo--roughly north from the Frari or Campo San Polo to Campo San Giacomo Dell'orio, then west towards Ponte Scalzi.
Cannaregio--basically the whole west-to-east length of the sestieri that is north of Rio della Misericordia, then all the way through the northernmost part of Castello. Pass through Campo San Francesco della Vigna, then head southeast towards the Arsenale. Then wander back to Campo Santa Maria Formosa.
Dorsoduro--start at Campo San Trovaso, head west towards Chiesa San Nicolo dei Mendicoli. Then, work your way roughly north and east towards Campo San Pantalon.
Also, head to Sant'Elena, at the extreme eastern end of Castello. Although the paths here aren't as old and windy as the older parts of Venice, you won't see many other people.