I disagree, forests are different all over. Oregon forests will be different than California Sierra forests, and within fifty miles even Sierra forests differ - as you go north on the PCT there are all kinds of changes in flora. The sequoia groves are awesome.
Loop hikes in the Sequoia/Kings Canyon would offer you a good variety tho - you can move through oaks to pines to sequoias to treeless alpine and back in a week, easy. Check out the High Sierra Trail (not the route) - there are shuttle options to get you back to the west side, or you can simply plan to fly out to Visalia, take the shuttle into the park, hike through to Mt Whitney and down to the portal, hop on CREST bus to an east side airport, and fly home. The time on the trail would give you a good opportunity to acclimate as you go, and if you had problems with high altitude sickness you could bail out north to Onion Valley instead of going to Whitney, or simply turn around.