Mt Goddard (4138m) is located in the Evolution region of the Eastern Sierra but
in a place very difficult to reach on a day hike whichever way you approach it.
Western RouteThe trailhead is at the Courtright Reservoir. Take hwy 168 east towards Shaver Lake but turn right before the lake into Dinkey Creek Rd that turns into McKinley Grove Rd. Follow the signs to Courtright Reservoir to the end of the road where the dam is. At the dam you get three choices: to the left you can drive the paved road to the expensive campground and to the Cliff Lake trailhead; straight ahead you do to the boat landing and to a free campground; and to the right you drive over the dam itself. Turn right, cross the dam and follow the paved road around the eastern shore to the dead end, which is the parking lot for the Maxson trailhead (roughly two hours from Fresno).
As of 2015 there was absolutely no sign announcing the trailhead, except for a sign "Trail". The trail starts by descending steeply to the dirt road down below (that goes to some campground). After about 1 km, another cryptic sign "Trail" encourages you to turn right into a trail. There is still absolutely no information about what trail that is. In fact, you don't get a sign with names until you reach the junction with Hobler Lake. Note that signs are posted very high on trees: if you are looking down at your steps you might miss the signs. Even when there are names, there are no distances. Turn right at the Hobler Lake junction (i.e. don't go to Hobler Lake) and continue towards Post Corral. In between you will pass the Long Meadows and a junction to Burnt Corral. From the Hobler Lake junction to the (big) creek crossing the trail descends nonstop. Post Corral is not marked anymore (the sign is there, nailed up on a tree, but you can't read what it says). At Post Corral the trail turns south and about 2 kms later it reaches that big creek crossing. On the other side there is a junction: go left towards Red Mtn Basin (which really means Fleming Lake). The trail now starts climbing. When the switchbacks end, the trail starts heading northeast. There are no tricky junctions and the foresty route is fairly uneventful until you reach Fleming Lake. After this lake there is a junction with the Rae Lake trail: go right towards Disappointment Lake. and Hell for Sure Pass. These names are ridiculous so we renamed them Tagore Lake and James Joyce Pass.
The trail does not coast Tagore Lake (3150m), but you will see it well. The trail now becomes an abstraction but usually there are plenty of cairns to guide you. You pass another lake, Chagrin Lake, and then trail begins the ascent towards James Joyce Pass. (3500m). On the other side the trail then descends east to an altitude of 3100m where it bends sharply south and eventually joins the the Goddard Canyon trail that coasts the Joaquin River at 3000m of elevation. Follow the Goddard Canyon trail along the South Fork of the Joaquin River to its source: Martha lake (3,354m). Then scramble up the west ridge of Mt Goddard which is mostly class 2.
We renamed "Disappointment Lake" as "Tagore Lake" and "Hell for Sure Pass" as "James Joyce Pass" but here is what your topomap will show:
Eastern RouteThe catch is to get on the John Muir Trail as quickly as possible and without too much elevation gain/loss.
One can start from the North Lake trailhead or the Lake Sabrina trailhead. The route from North Lake might be easier to follow but it involves a massive elevation gain and loss. The route from Lake Sabrina involves a lot of bouldering and requires good scouting skills but it is shorter and a bit less demanding.
The trailhead for the Lake Sabrina routes is located before the Lake Sabrina dam on the left-hand side of the road. There are very few parking spots and overnight parking is not allowed. There is free parking on the road near the campground (about 1km before the dam).
Lake Sabrina is located at the end of 168, west of Bishop, about 1.5 hours driving time south of Mono Lake, i.e. 6/7 hours from the Bay Area. From Bishop, take 168 west, aka West Line St, all the way to the end. See the page for Mt Darwin's Western Face for how to get from Lake Sabrina to Haeckel Pass or see the Wallace Pass page for how to get from Lake Sabrina to Wallace Pass. (I don't recommend the route via Echo Pass to Wanda Lake because in my opinion Echo Pass is class 4).
Either way, descend whichever canyon you are into to the John Muir trail, and most likely you will hit it at Sapphire Lake.
If instead you started at North Lake, see this page for how to get from North Lake to Lamarck Pass to Darwin Canyon and to the JMT, then just go south through Evolution Lake and Sapphire Lake.
Follow the John Muir trail south to Wanda Lake. From the southeast side of Wanda Lake hike cross-country south to an obvious pass, Wanda Pass. On the other side there's a lake. Head east from either Wanda Pass or from that lake to Mt Goddard, easy class 2.
Camping at Courtright Reservoir
There is one expensive campground ($24 in 2015) just before the Cliff Lake trailhead. Everything else is free as long as you can park safely and as long as there is no "no camping" sign. The whole east shore up to the parking lot is free camping (NOT the parking lot itself). There is potable water at both the expensive campground and the free campground.
Camping at Lake Sabrina
There is a campground just below Lake Sabrina. There is free parking outside it. There is a tiny space at the trailhead for day hiking.