I don't know the exact conditions this year but a few options that are usually pretty clear by now are:
White Knob traverse: Four prominent 11k peaks all nicely grouped together on pretty easy terrain. I did it about this time of year in 2010 which was a little bit of a heavier snow year. We had no trouble with snow.http://www.summitpost.org/white-knob-mountains/633978
Smiley Mountain: A big 11k peak in the Southern Pioneers, close to the White Knobs. It has a broad Southern exposure that usually melts out pretty early. This peak is also pretty mellow terrain-wise.http://www.summitpost.org/smiley-mountain/447372
Big Black Dome: Another mellow terrain 11k peak that melts out pretty early. It is in the Copper Basin area of the Pioneers, across from the White Knobs.http://idahosummits.com/big_black_dome/big_black_dome.htm
Grays Peak: A 10k peak, also in the Pioneers that is usually pretty clear by now. It is near the main crest area and is accessed basically the same way as Hyndman, just continuing up the East Fork road a little farther to Federal Gulch CG.http://idahosummits.com/grays_id/grays.htm
Phi Kappa/Summit Creek Peak: Also in the Pioneers but accessed from Trail Creek Summit. Killer Views and pretty mellow terrain.http://www.summitpost.org/phi-kappa-summit-creek-peak/153192
Smoky Dome: A very prominent 10k peak just North of Fairfield. You can do a traverse of nearly the entire range in a day (Smoky Dome, 3rd, 2nd, 1st peaks)if you have two cars. I did it in June of last year, which was a pretty heavy snow year, and we were clear pretty much the whole way.http://idahosummits.com/smoky_dome/smoky_dome.htm
There's tons more. If none of these fit the bill I'm sure we can find more. Let me know.