I'm on the west side of town and you're talking east side so I can't give much advice, except my experience driving on University is that it is very heavy traffic and not bicycle friendly and I personally would not bicycle on it.
The Denver Bicycle Touring Club has a map that shows the best routes. It's available at bicycle shops and REI. The DBTC has worked with city planners and experienced bicylists who review the routes. I personally know some of the cyclists who have approved the routes.
We personally don't go in unfamiliar areas of Denver without the map because of, construction, car accident, etc. The map was updated within the last year.
My SO was not impressed with goggle maps, it routed him on roads he knew were unsafe, but he has not tried to use it recently. In his opinion some of the routes were illegal and dangerous. We're not sure if they've fixed their problems, ie, they routed bicyclists on route 6 through the tunnels, which is illegal for bicycles, but I still feel skeptical since I don't know the local presence.
Personally, I don't know anywhere I would ride University except on the sidewalk.