I definitely
do not look for bicycle paths!! I try to avoid them as much as possible. I can only think of one occasion where a bicycle path was decent, and that was the tow path along the canals between about Nancy and Strasbourg in France. Those tow paths were lovely. Anywhere else I've been, however, the bicycle paths have been pretty much useless. And it simply does not occur to me to look for bike infrastructure. In fact, I so rarely see bike infrastructure anywhere I ride, that when I encounter it, I take pictures of it because it amuses me.
When Rowan and I look at a map of Victoria (our State) to decide on a place to go, one of the things we look for are roads heading out in different directions from our "hub" so that we can ride one direction one day, and another direction another day. Ideally the roads should be somewhat more minor roads, not busy main roads, but if some of the riding will be on a main road, that's OK too. We might also look for a spot with some variety ... something different from where we usually ride, and perhaps also the possibility of riding in different scenery in each day of our tour.
And OP ... don't rule out the possibility of taking train or airplane somewhere ... or driving somewhere in order to see some new areas and ride on new terrain.