Peter Croft's "The Good, The Great, and The Awesome" and John Moynier and Claude Fiddler's "100 Best Climbs in the High Sierra" are great guides to this stuff even though they run from 3rd class up through 5th with probably the largest number of routes solidly in the 4th and very-low-5th category. Nonetheless these books do contain more of what you're looking for than any others that I know for the Sierra. Frequently the 3rd class route you want will be given a brief positive note as a good neighboring alternative or descent route for one of the 4th or 5th class routes that they spotlight.
In the meantime, for a quick hit, here are just the first ones I could think of off the top of my favorites list.
Laurel Mountain, just north of Mammoth, accesed via the Convict Canyon trail. There are two very brief spots (like ten feet) of 5.6ish and then the whole rest is very pleasing 3rd class. About 4000' and a great view. Descent is 2nd class. Bring long pants and scree gaiters for the descent This one's in Croft.
In Tuolumne Meadows, large parts of the Cathedral Range make a fabulous traverse, with options to challenge yourself over the highest points or traverse a little lower where you want to keep the exposure down. Take the Budd Lake approach to Cathedral Peak. Actually if you want to make a big big day of almost the entire ridge, camp at Budd or above. Do the 3rd class route on Cathedral. Hike up the connecting ridge (1st-2nd class) to the Echo Peaks. Around 5? are 3rd class, another two are 4th, and two more are 5th, so do the ones that look fun. Continuing east, the next crest is a cool 3rd/4th traverse on much nicer granite than the Echos. Then the Cockscomb and the Unicorn are lots of fun by any route you find.
Also out of Tuolumne: On the west side of Mt. Conness, if you look far enough to looker's/climber's left of the West Ridge proper, you'll find 3rd class gullies that stay 3rd almost all the way to the summit. Beautiful rock quality there and amazing views.
From Mammoth Lakes, head over Minaret Summit and park at a trailhead down by the San Joaquin River and hike out to the saddle between Mt. Ritter and Banner Peak, then climb both. Banner is an obvious 3rd class scramble up giant-stair ledges and boulders from the saddle; for the John Muir route on Ritter study a specific route description since it's a little hard to determine the exact start but then it's 3rd and quite nice (though it's very easy to wander into 4th, so keep your senses sharp). The summit of Ritter is a place not to be missed by any Sierra mountaineer.
Farther north, out of the Bridgeport area, Matterhorn Peak and Whorl Mountain both have enjoyable scrambles, but I haven't done them yet.
Heading south again... for a real fitness challenge, begin at sunrise at the foot of Nevahbe Ridge which is immediately southwest of the neighborhoods of Crowley Lake / Hilton; you can start from near the McGee Creek road. Climb the entire ridge. Takes an hour of scree and sand to really get up on it but after that it stays 3rd with varied and interesting changes of rock type for literally a mile or more of ridge. Don't stop until you summit 13,005' Mt. Morgan North. Either retrace to descend, or descend Esha Canyon. Bring many changes of socks and something like six quarts of water for this one.
Another similar "big day" is any of the ridges on Mt. Tom... super view from the top and lots of mining relics to be found on the way up.
Also in that category is hiking up the Morgan Pass road from the Pine Creek Mine, to go way up behind the Wheeler Crest and explore some of the other old mining terrain up there. You can summit numerous interesting peaks and subpeaks from there and you're guaranteed to have a day full of mining history.
Up Rock Creek there is a lot for you to do. Bear Creek Spire is fun by Ulrichs (sp?) route: you first ascend to the Sierra Crest via a col at over 13,000' and then turn left on sand and talus to a point a hundred yards below the summit and then do some interesting and convoluted route finding. There is in fact a 3rd class route though it borders on 4th. The final summit is a single boulder with an exposed move, but people still consider they've climbed it if they skip that.
There are numerous other good 3rd class routes on the 13ers of Rock Creek.
Or backpack up the Pine Creek trail and then take the cross-country route from Honeymoon Lake up to the Royce Lakes and camp, then the next couple of days you can summit Merriam, Royce, and Feather peaks all by 3rd class routes. In many years you'll want an ice axe and instep crampons or enough of a boot to kick steps in the snow between the peaks, since you typically climb them from the cols in between them. Although I'd also like to try just the northeast(?) face of Merriam from the lake below it, which looks 3rd+.
Mt. Darwin has a fabulous, airy, yet still truly 3rd-class-only route to its summit plateau. You don't get the true detached summit pinnacle unless you're willing to solo or belay a very small bit of 4th-5th, but the plateau is more than worth it. It feels like you could be on top of the pre-glaciated roof of the Sierra.
Many other Evolution area peaks have great 3rd class routes.
In the Palisades, the northeast face (Norman Clyde route) of Middle Pal is fantastic. Requires an overnighter unless you're up for a really challenging day with nearly 7,000' gained and lost. Doing the route strictly by-the-book keeps it 3rd, while it has the cool property that just a few feet away is much cleaner rock that goes at 4th, so you can adjust and find a happy line between the two.
Also in the Palisades, out of Big Pine you can take the north fork of Big Pine Creek (same as if you were heading for North Pal) and take the Yellow Brick Road route on Gayley Peak. Gayley is perfectly positioned for a panoramic view of the whole Palisades amphitheater, both North and South forks of Big Pine Creek. It sits above Temple Crag but below Mt. Sill and sticks out where you can see it all. Some years you need an axe for just a bit while getting up to Glacier Notch from which you turn and climb the ridge to Gayley.
There's a LOT more between the Palisades and Whitney, but most of it still on my to-do list. One more than comes quickly to mind, all they way down in the Whitney zone, is the 3rd class routes on Mts. Russell and Carillon.
Oh yeah, here's an unusual and rarely mentioned one. People talk about Charlotte Dome for its 5th class south face routes, but for an avid 3rd-class scrambler climbing its descent ridge is a real treat. It's one of those routes where it's just so cool that it "goes", that it's even possible. Where if anything was taken away it would go to 5th. And the summit is really something else, with big sunny ledges, crazy potholes, a ridiculously amazing view out over Bubbs Creek Canyon and out toward Mt. Brewer, and several places where you can pop through holes behind or beneath a giant block and come out on another side with another view. Well worth the 12 mile hike over Kearsarge Pass. There is good camping at mid-height of the dome just east of it near a spring. The last 3 miles of trail to there from the east are basically lost and you have to find them again. It's an old abandoned trail to the once and future Gardiner Pass. Otherwise you end up along the stream at the bottom of the Charlotte Creek canyon and then having to bushwhack up to the dome.
Whew! Nuff for now, that oughta hold you for a while. Have a great summer out there!