I very much want to backpack a few miles into the wilderness somewhere (preferably in Canada), setup camp, fish, and not see another human for several days.
I tried northern Manitoba this year. The country was beautiful, but the trees were so close together I wasn't able to hike through them. As Manitoba is reasonably flat, the trees grow all the way into the water at most lakes, so there was no way to get to the water. If I had, I would have been camping half in the water.
How do I find a remote area, without people, and with a reasonable assurance I'd have dry space to setup camp, with access to fishable water?
Loc: Portland, OR
I don't live or hike in Canada, so I can't just direct you to a lake there that meets your qualifications. I can give some hints, based on my general experience.
First, fishable lakes that have reasonably short trails to them and decent campsites beside them are common enough. But that combination of factors is rather attractive to a lot of people, so your other qualification of not seeing another person for many days together doesn't fit very well with those other listed desires.
There are some strategies you could employ to increase your chances of not seeing others at an attractive spot. Choose a time to go that other people are less likely to choose. Weekends are very bad. Mid-week days are somewhat better. Even better, go when there are clouds of mosquitoes at your destination. Or bad weather, such as continuous rain and cold.
You could choose a lake that is very far from any roads, so you must hike a very long distance, preferably uphill, to get there. About 15 miles should be enough to discourage most others from ruining your solitude.
Additionally, you could choose a lake where the access road to the trailhead is horrendous, rutted, rocky, dusty, narrow, and very long. This helps screen out less intrepid fishermen, but does not present any strong guarantee you won't be joined at your chosen lake. 4-wheel drive, high clearance vehicles are too common for that. Going somewhere quite distant from any sizable city also helps.
You could choose a lake with no trail access at all, requiring extensive cross-country travel to reach. Surprisingly, such lakes will sometimes have established campsites anyway. You'll just have to trust there will be fish to catch when you arrive.
Or, you could choose a fairly large lake and just accept that you might have to share it. It is my experience that anywhere attractive enough for me to want to hike to will also be attractive enough for others to want to visit. I have used most of the above-mentioned strategies, singly or in combination, and they do increase the chances of solitude. They never guarantee it. Good luck.
Look at the Algoma Central Railroad out of Sault St Marie Ontario. The trail will drop you off anywhere along the way and you can flag it down again to get back. It is the passenger train not the tourist train.