For April or May, you should look at lower elevation stuff. Most of the trails around Tahoe will still be under snow. Yosemite Valley, for instance with the waterfalls roaring, but the road to Glacier Point and the hikes up there won't open up until sometime in May or early June due to snow. Or wait until the fall when the temps cool down and all the high elevation stuff is still open.
I did a lot of hiking there in the '90s - early '00s renting a place at Mammoth Lakes. Lots of great hiking both north and south. There is a timeshare near June Lake, but it never seems to be available in hiking season and wasn't that appealing. Mammoth has a lot of condos and house rentals which have gotten more expensive in the last 15 years but It has the most options and makes a good base. Fall/Sept is a great time but the weather can turn in early Oct. The big thing to remember is that much of the hiking is at 10000' and getting acclimated and how you personally react to altitude is a major consideration. But the aspens turning and the scenery is just spectacular and there are lots of good hikes that fit your criteria.
