It looks like I'm going to have about 4 days in CO the end of June or first week of July. I'm looking for a couple of "iconic" or classic climbs, either snow or rock. Snow with some ice would be great, any chance of Dreamweaver being in at that time? Or perhaps some alpine rock up to 5.6 o 7. North Ridge of Spearhead looks fun. Preferably within reasonable driving distance (3-4) hours of Denver.
Any thoughts or input would be appreciated.

RMNP has been extremely dry. Unfortunately, Dreamweaver might not come into shape at all this year. As of now, it's a very narrow strip of snow. You might enjoy Kiener's on Long's Peak and there's the Northeast Ridge on Sharkstooth (5.6). It's on my list of climbs to do, but the Southeast Face of Taylor looks pretty sweet and is kind of what you're looking for.

I suggest you browse around the Climbing Life website. The RMNP Alpine Routes page lists a lot of the classic easy/moderate routes.

Good suggestions from JonW. For snow, I would consider Superstar on James Peak, Notch Couloir on Longs, Taylor Glacier, and North Couloir on Pacific. (They are all within the desired distance.) As the time approaches, you may get more reliable information on their conditions. For rock, also consider Pagoda's North Ridge and Spiral Route on Notchtop.

For rock and for scenic beauty, I would suggest Devils Thumb and Lone Eagle. Both are very beautiful and both have several technical routes.

Devils Thumb:

http://www.summitpost.org/devils-thumb/154398

Lone Eagle:

http://www.summitpost.org/lone-eagle-peak/154100

Thanks Jon
Spearhead is on my list. And Taylor looks interesting too.

Also check out Blitzen Ridge on Ypsilon, and the NE Ridge on Sharkstooth. Both are classics and on my tick list for this summer.