Other trailheads: Elkhart Park and Big Sandy
Both are crowded (I counted over 100 cars at the Big Sandy trailhead when I was there), but there is a lot of territory for the crowds to disperse and disappear! For example, Island Lake, Titcomb Basin and the Cirque of the Towers are popular, and deservedly so, but you can take a look and then go to far less crowded areas. The "back side" of the Cirque of the Towers (Shadow, Billy's and Texas Lakes) is, IMHO, just as spectacular as the "front" and far less crowded. Plus you can go over Hailey and/or Washakie Passes, and/or take a side-trip into the spectacular East Fork Cirque.
Check out the New Fork Plateau trip when you get Nancy Pallister's book! She shows an easy off-trail trip which eliminates having to go back down the 2,000 feet you climb on Day 2. Thanks for the link to Ronald's report, which I missed.