East Face to South Ridge
From the east, Three Needles looks like it may have some trials and tribulations in store, but a straightforward route exists that gains the South Ridge .2 miles from the summit. From the ridge crest, the summit is .2 miles away and a short simple scree section is followed by a quick scramble to the summit, bypassing towers en-route.
East Face - Route in Yellow
For Three Needles alone (or with "T 11") the route starts from the end of County Road 65 which begins just south of Red Mountain Pass. Rd 65 continues up from Hwy 550 2.5 miles, but there are signs indicating unsafe travel well before then. Proceed at your own risk with a high-clearance vehicle if you so choose. Parking at the junction of 65 and 16 may be a more prudent choice, and allows for a reasonable spot to return to if you are planning a loop hike ascending more peaks north of Three Needles.
Just before the scrambling section on the west side of the ridge
At the end of the road at about 12,300', follow gentle scree and grass to Porphyry Basin directly below Three Needles. Follow scree and talus up to a gully that retains snow into August. Class 2+ scrambling on the right side of this somewhat loose gully leads to a scree-based section of the ridge, where the route stays on the west side of the ridge the remainder of the route to the summit. The route-finding is rather straightforward, and breaks in the cliffs are easy to find near the summit block. Return your ascent route to the top of the East Face gully you ascended and drop back down or stay on the ridge and traverse to "T 11" if it is on the agenda. If the latter, the gendarmes on the ridge between "T 11" and Point 13434 should probably be skirted to keep things reasonable.
The route could be more complicated in the early season (May through early July), when crampons and an ice axe are recommended. A helmet may be advisable in larger parties as rock is somewhat loose on the east gullies.