weather.gov is pretty decent. Lets you pinpoint an area on a map for a forecast.
Acclimate if possible. Hydrate.
Summit the more popular mountains first, then work your way to the more obscure/less traveled ones. Should something happen, you're going to have an easier time getting assistance on those than one that's infrequently travelled.
There's still a lot of snow up high. Still rideable (snowmobile) snow up on Jones/Corona pass. Last I heard Cottonwood pass is still snowed in. I'm not sure about Vail pass, if shrine pass road is driveable or not yet, but that's a good indicator for the summits in that area.
There's a webcam and weather station up on Pikes Peak. I need to hit that (pic related) on the moto this summer and drag the Nikon along for the ride.
You're still going to find snow in july/august. Right now? I'd wait.