The Muir Wall is an outstanding route that follows a beautiful natural line of crack and corner systems just left of The Nose. Although moderate in grade this route sees relatively little traffic due to it's very sustained and demanding nature, which requires lots of technical aid climbing. This route has been climbed at 5.9 C4 but most parties will probably want to bring some pins and a hammer to keep the grade at A2. For more detailed info and topos look at the "Yosemite Big Wall Supertopo" guide book.
Location
The approach is the same as The Nose but once at the base of the wall continue west till you come to a large left facing dihedral just left of Moby Dick (Moby Dick is a good alternate start for the route). This approach should take about 20 to 30 minutes with a haul bag.
Protection
Bring three sets of cams from .5" to 3", extra 1" cams and one each of 3.5" to 4.5" a 6" cam and micro cams are also very useful on many pitches. Also bring two sets of nuts with offsets and one or two sets of micro nuts with offsets. Bring one cam hook, an assortment of about 8 to 10 LA's, a few 1/2" and 5/8" angles and a sawed off 3/4" and 1" angle. Finally bring 2 to 4 KB's and Supertopo says to bring a Beak but I don't recall ever using one on the route.
We did this route clean several years ago and I highly rec an arsennal of small aliens, both offset and normal. The crux is a little bit rotten.
Overall a super classic route. One of the best bivies on the Cap is to the left about 80' of the start of the huge dihedral near the top. Some funkiness to get there (easy 5th traverse) but oh so classic....