Let me say right off, this is not an attempt to discourage you.
Lake Coeur D'Alene has what you are after, it's deep with a high flow-through. It's a rare season it freezes over the deep water enough for safety afoot!
50 miles north, at Sandpoint is Lake Pend Oreille, 107 miles around, eleven hundred fifty three feet deep in one spot. RARELY is it safe except in a few shallow bays, has flow-through from the Clark Fork River via the Cabinet Gorge Dam (hydro electric). The larger fish are out there at distances up to several miles and often far down.
The best time for large fish is unfortunately open water.
Many small lakes have easy access but, wall hangers are rare.
Timing is always a guess so, if the fickle weather is summer style, plan on a boat.
The lake record here is a bit over 37 pound rainbow.
The beautiful area is astounding.
Good luck, bring a camera.
Enjoy.
Tom