I am certainly not an expert on the area, but have fished there. First of all, forget the Merced River within the park. It is way to crowded. It gets better just outside the park but access can be tricky. If I was fishing Yosemite, I would head to Tuolumne Meadows and fish the Dana Fork and Lyell Fork, upstream from the meadows. You will get away from the crowds. The area is not a dramatic as the valley, but the scenery is nice and the hike along the Lyell is beautiful. Both are relatively small streams and hold smallish brown trout. I had good luck there and was glad to get away from the madness below.
Just an aside, I have a bear picture that is going to be published in a book about Yosemite.