Cube Point is one among the many "cragging" peaks north of Cascade Canyon in the Tetons. From the valley it is an indistinct bump, much like Ice and Storm Point. However, from Arrowhead Lake, it is somewhat more impressive. The East Ridge is an enjoyable 3-5 pitch jaunt up good rock. Alternatively, a scramble can be made up the East Couloir, a 4th class climb up occasionally loose rock. Cube Point makes an excellent rest day destination, and gets climbers into a part of the park that they may not have seen before. In addition, the views south over Cascade Canyon toward the Cathedral Group are among the best in the park.
From Jackson Hole, drive north into Grand Teton National Park and follow signage to the Jenny Lake parking area. Walk west past the ranger station and other cabins, until you find the boat docks. A boat ride is $5 each way, or $9 roundtrip if purchased in advance, if I recall correctly. Alternatively, you can hike around the lake, which is around 3 miles one way. Once you arrive on the other side of Jenny Lake, head north along the lake shore until you find a fairly distinct climber's trail (unmarked!) heading left and uphill. The trail switchbacks a bit and begins to climb up into Hanging Canyon, passing Ribbon Cascade (which will be visible fairly shortly). Follow the trail above Ribbon Cascade and into the hanging canyon. Cube Point will be to your left (south), and if you walk in that direction, you should see an arrowhead-shaped pond/lake just below you. Pick your away around the pond (there should be a climber's trail in this area) toward the east ridge. From here you will want to enter the couloir/gully to the east of Cube Point. At this point you can continue up the gully to the summit using the Class 4 East Couloir route, or gain the 5.4 East Ridge.
No permits are needed, but an entrance fee is required for the national park, and the boat ride across Jenny Lake costs ~$10--it is optional, however.
This, like most climbs in the Tetons, is best done in the summer. Cube Point is at a lower elevation than most of the range, so its rock will dry out earlier, and could be climbed comfortably in June. However, the approach and descent gully will probably still have snow at that time. Nonetheless, this is a great early season climb to warm up for the summer alpine season.