I'll be in Colorado for a couple weeks at the beginning of June and was wondering what the conditions are looking like? How's the snow been this year? I'm pretty new to climbing and looking for some easier class 2-3 climbs to do.

Anything specific you're looking at?? In early June (in my area anyways) you should be snow free up to 11,000 feet on south facing and west facing (east of the continental divide) slopes, you will probably need snowshoes after that. Its been a pretty average year for snowfall but a couple of systems within the last month have certainly not helped.

Snowpacks in the northern part of the state are generally running 150 to over 200%. Central conditions are closer to 130 to 170%. Southern snowpack is lower, generally less than normal at 75 to 110% depending on where you are. Upper Rio Grande drainage seems to have the least snow.
Early June 2011 in most of Colorado's higher elevations will still be a snow experience.
Good luck!