Drive North on the main highway (89), then turn onto the Rockefeller Highay at Moran Junction. There is a large parking area just before the bend in the river.
I arrived in the park on the previous day, and a heavy rain storm was just breaking up. The aspens were at peak color, so it was THE place to go for sunrise. Although you get the added interest of the aspens in fall, it also brings a lot of people to this spot. Get there 30-40 minutes before sunrise to get a spot you want.
Mount Moran breaking out of the strom clouds just after sunrise at Oxbow Bend.