You've gotten some good info already I can't remember what places are close to Mammoth, but I think Lee Vining and Tom's Place are near there with some decent fishing. Sometimes they put Alper trout in the streams which are huge, 5-6lbs.

Bishop creek can be good, but it's often crowded. I like to go up to the lakes and fish the inlets. All of the lakes Sabrina, South and North are beautiful and close to one another. North is my favorite but the drive up it is kind of sketchy. It's a steep dirt road with a drop off on the right. Not the greatest for passing other vehicles. You can also check out Rock Creek. Rock Creek Fishing Information

Like you I mostly fished with lures when I went there as a kid. Most of these creeks are gonna be tough casting. The Owens River has big trout and places for fly casting. I never had much luck there, but I've seen pictures of huge brown trout caught from the river.

Flies that always worked for me were black ants, mosquitos, adams, and black wooly buggers. I would try a white crystal bugger.
It works great for stocked trout here in NC. The creeks are some what similar.