Here in Scotland, i'm used to walking all day in wet footwear. Even without river crossings, the ground is usually boggy.
I always look for quick draining synthetic uppers in my shoes, preferably mesh. Sometimes the shoes will never dry out completely. I started wearing Inov8's around 5 years ago, but they didn't prove durable enough for my off trail hiking. I often have some scrambling on granite in my routes though. I also have a wide forefoot, so only a couple of models (295, 330) suited my feet. Nothing wrong with the shoes, just my use.
I prefer merino socks when my feet will be wet all day. I find them more comfortable than synthetic.
The shoes i use most are Mizuno Wave Harriers. Someone said on another thread that they are difficult to source in the US.