At the risk of gross generalization, I tend to find rainbows in the faster water, i.e. seams where current enters pools, riffles, pocket water in rapids, etc. I tend to find browns and brookies in deeper and slower water, especially with a mess of down wood. Find a good logjam at the corner of a big bend pool, and often that's where they'll be.
That's only part of it, though. If you want one kind of trout or the other, you have to fish where there's a population of them. My home water, for instance, as about 8:1 rainbows to brookies, and very few browns. I've heard rumors of them, but never caught one there. Anyway, you don't go there to catch brook trout.
You'll find rainbows and brookies sharing the same reach of stream, or rainbows and browns, but more rarely browns and brookies. The browns seem to bully the brookies out of the good spots. Around here, at least, what tends to happen in streams with both is that the browns get the big valley water, and the brookies get the headwaters and freestone tribs. If you want mainly brookies, you have to find a stream that they have pretty much to themselves. That goes double with lakes and ponds -- they don't do very well against other fish.
When targeting Brookies by me your targeting Natives. The streams with the good populations of natives are generally the out of the way trickles that see few fisherman and usually have never seen a stocked trout either. So in that sense if you fish one of these streams chances are you will catch a Brookie.
In the streams where natives exist where other trout have been planted they tend to be everywhere the transplants are not. Under boulders and undercut banks , in brush and tiny pools.
In lakes by me where they stock Brookies they all stay together by water temperature as they adjust to the environment. One particular lake in April they are in the spot they were stocked., in May they are all around the boat ramp and by June they are at the mouth of the feeder stream trying to join the native population!
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It's a tough question that I believe the answer will be different from region to region.
"I was born to fish" Lee Wulff
"There's more B.S. in fly fishing then there is in a Kansas feedlot." Lefty Kreh
" It ain't over till it's over." Yogi Berra
"Your not old,you've simply acquired a patina." Swirlchaser
Around here, if you fish lower elevation, you get mostly browns. Moving upstream one finds rainbows mixed with browns. Next the brooks and cutts get mixed in. Around 8000' in Colorado one can get a 'Grand Slam' all four species in one day. Above 8000' one will mostly find brooks and cutts. Beaver ponds hold brooks for sure up high. High lakes hold almost exclusively brooks and cutts.
Some high lakes are loaded with brooks only, some lakes only have cutts. Both fish are very eager to eat smaller bushy dries (elk, deer, foam, etc.) and will also eat smaller 16-20 nymphs. Neither are very picky, as long as you don't spook them.
I define 'targeting' brookies as going to a water that holds mainly brookies. I fish a small tailwater in Idaho that contains a beautiful reproducing population of rainbow trout, along with a very small population of brook trout. I fish as I would for all trout in this stream as there is not a preferred method to fish just for brookies.
Also, out west when you say 'natives' we are talking about cutthroat trout, not brookies. While cutthroats are a sucker for a well-presented dry fly, there really is not a differentiation in methods to catch them, bows, browns or brookies. They all eat the same things. Just my take on it.
So, to sum up, if I am targeting brookies, I go to brookie-holding waters and don't necessarily change my tactics to catch them.
P.S.: I do change tactics if I am after big brown trout in larger rivers. I usually end up using big streamers on sinking lines as they do tend to hold in deeper holes and get pretty voracious for minnows, especially starting this time of year on into winter.
It's really fun when you find an unfished population of native brookies. They can be amazingly naive. I fished a small trib yesterday with about a 50/50 mix of rainbows and brookies. One of the brookies tried my indicator first, then hit my split shot, and finally took the caddis emerger. Wow.
Only place I've targeted them is in Jellystone. There, it was small slowish water around structure like log jams and the like. Plenty of that in the creek we fished as there was plenty of downed timber from a forest fire a few years back. I also had good luck on the gaudy stuff. Things like royal coachmen wets and royal Wulff dries. They seemed to key on those more than the Adams/elk hair caddis patterns. But we didn't hit during a hatch either.