Ok, I gotta nominate my eponymous peak, Mt. Ritter. To keep within the rules of being "just a dayhike," I'll offer two alternatives, both starting from Agnew Meadows. The simpler one, an out-and-back to Ediza Lake, would be about 15-20 miles, depending on where you turn around. 20 would take you right to the base of Mt. Ritter, where 15 would stop somewhere by Ediza. The views from Shadow Lake are spectacular and getting up close to Ritter and neighboring Banner Peak just above Ediza Lake are dessert. The alternative (and might be pushing the 20-mile limit) would be to hike up past Ediza then up and over the ridge above Nydiver Lakes and down to Garnet Lake and then back to Agnew Meadows. Has the advantage of less backtracking (just the first/last couple of miles between Agnew Meadows and the San Joaquin River) and seeing a different stretch of countryside on the way back. For shots of the trail, Shadow Lake, Ediza Lake and Ritter/Banner, see the "Mt. Ritter" section of my WWW site
Closer to home, the elevation is neither so high nor the gains so great but even the Ozarks have some nice trails. Three favorites include:
The Taum Sauk stretch of the Ozark Trail. Goes from Johnson Shutins to the top of Taum Sauk Mountain (1772.68' and the highpoint of MO). About 15 of the toughest Ozark miles you'll ever put in. Rocky ridges, sumac glades, creek valleys. You pass by Mina Sauk Falls, the tallest waterfall in MO (see my VR pan
of the falls) and on up to the summit of Taum Sauk. Strictly a point-to-point trail, so you have to spot a vehicle at each end, but it's a great training hike for taller stuff out west, given the obvious limitations in absolute altitude.
The Bell Mountain Wilderness Trail. Not that far from Taum Sauk and also along the Ozark Trail, you can hike Bell Mountain either as a point-to-point or a nice 10-mile loop. Bell Mountain is 1702', so nearly as tall as Taum Sauk. The glades along the ridge are exemplary and the trail takes you over the top of Bell Mountain, down into the neighboring valley and back up to the trailhead. A very nice fall hike when the leaves are changing.
The Whispering Pines Trail at Hawn State Park. Just about an hour south of St. Louis, this 10-mile loop meanders through some of the most varied topography and forests you'll find in the midwest. Alternately hardwoods and native short-leaf pines, up and over ridges, meandering along creek beds (with beaver-gnawed trees), and up to the top of Evans Knob for great views of the surrounding hills, this trail is a real favorite in the spring when the dogwood and redbud are flowering. There are a couple of back-country campgrounds along the trail, so you can also use it for a short two-day backpacking trip if you so desire. I've probably hiked this trail 10 times over the years and I still love it...it's my favorite day hike in MO, partly because it is
a loop, so I can easily solo it but also because it includes about 2,000' of gross vertical, so you get a pretty fair workout by midwest standards, as well.