I spent a year once in Klamath Falls, Ore. It (Oregon) was an outdoorman's paradise. Elk, mulies, whitetail, blacktail, bear, cougar, pronghorn, bighorn sheep, largemouth, smallmouth, crappie, walleye, and trout. Plus the usual small animules and upland game birds. Excellent mountain biking, with multiple trailheads converging on the city park.
To directly address your requirements,
1. It's on the shore of Klamath Lake and the Klamath River runs through town. There's no more falls because a dam backed the water up above where they used to stand.
Just don't drive anywhere any body of water at sunrise or sunset when the weather is warm. The midges hatch by the billions, and form thick swarms that easily are mistaken for columns of smoke rising from a fire. Driving through a swarm of them makes your windshield look like you'd poured a gallon of mucilage on it. Gas stations leave buckets of windshield washer and a squeegee at curbside because your windshield washer/wipers won't touch these bugs, and they want to keep you away from the pump islands if you're not there for gas. The blessing is that the fly fishing gets crazy in midge season.
2. It has a hospital, about 100 beds. Never had to avail myself of its services, so I learned nothing about it except its location.
3. It's primarily a farming community. Should be no problem finding a small farm.
4. Population right at 20,000. It has a Super WalMart, a Safeway grocery, all the customary chain hamburger joints and a few tony restaurants. The nearest town of population 100,000 or more is 75 miles and three mountains away, so there's no spill-over crime. It's so "Mayberry," the downtown merchants still can leave merchandise on the sidewalk in front of their shop and not be robbed blind. When I was there last, downtown parking was still free. Also has a commercial airport with daily service to Portland, Seattle and San Francisco.
If you need a dose of culture, Ashland, Oregon's "Key West," and home to North America's oldest Shakespeare festival, is 65 miles away.
5. It's on the leeward side of the Cascades. The weather coming in from the coast drops almost all its moisture on the windward slope before it gets there, so average annual rainfall is very low, only 13". That's only 3" more than "official desert," but the area is verdant green because the snowcapped mountains feed the streams and rivers year-round. However, water rights are a running gunbattle.
That's the good news. The bad news is it also averages 36" of snow. I once saw three feet of snow on the ground, but they never closed public schools on account of snow. They run the snow plows and the gritting trucks early and often, so city roads (and the surrounding county) are never impassible. Long-time residents put snow tires on all for corners of their cars on the first of October. I got by with tire chains, fronts-only, on a front-wheel drive car. But winters aren't so bitterly cold. Even with snowfall on the ground, it rarely was below freezing, and I never saw it below 10°F. But there's also plenty of natural snow for all the ski resorts.
The ground never freezes because the Cascade mountains are volcanoes. So geothermal home heat also is an option. Vocanic soil makes for great agriculture, incredible potatoes, and the stickiest goddam mud I ever have experienced.
Summers are incredible. Robin's egg blue skies and sometimes there won't be a single cloud for weeks on end. Highs in July and August are mid-80s, virtually no humidity, but it cools quickly when the sun disappears behind the mountains for comfortable sleeping. My house wasn't even airconditioned but I didn't miss it. Most days you can see snowcapped Mt Shasta in northern Cali, which glints in the sun and looks like a 14,000-foot tall klansman's hat.
The only reason I haven't gone back to live is that the state's political climate has had an unfortunate change of complexion since I left. In accordance with Lowlight's ban on political discussions, that's all I'll say on that matter.