Finding trout can be difficult. One way to help focus your search could be as easy as knowing the conditions various trout species thrive. A few years ago, I emailed a fish biologist who use to blog at the Fish Creek Blog. His reply was very informative:
Basically, there is not much difference between brown trout/brook trout/rainbow trout habitat. All are stream and lake dwellers that prefer cool, oxygenated water, invertebrate and/or fish as prey, and require gravel substrate in which to construct redds, or gravel nests where they bury their eggs.
There are some differences between the species, however. Brown and brook trout are fall spawners, and their eggs incubate throughout the winter and hatch in spring. Rainbow trout spawn in the spring around the time of peak streamflow and fry hatch out during the summer. Brook trout are known for spawning along lake-shores in areas of groundwater inflow, and also tend to seek groundwater for spawning in streams more so than other species.
In addition, you are right that brook trout can tolerate acidic water more so than other trout species, likely a result of the conditions from which they arose in eastern North America.
The source of brown trout that were introduced to the U.S. came from stock in English, Scottish and German chalk streams and these fish tend to do much better in productive limestone streams.
As far as lake trout are concerned, they are usually a lake obligate species (some do live in streams) and require deep, cool, well oxygenated water. As adults, they feed mainly on fish and therefore require lakes with abundant forage fish in order to grow well. While the other trout species you mentioned construct redds, lake trout usually spawn on windswept shoals in large lakes and deposit their eggs between the cracks of rocks along these shoals.
Another interesting thing to note is that lake trout (salvelinus namaycush) and brook trout (salvelinus fontinalis) are char, while the brown trout (salmo trutta) is considered a salmon, and the rainbow trout (oncorhynchus mykiss) is considered a true trout.
Thanks for your response Jeremiah!