Hi rtzui, weather should be absolutely lovely next month.
I would go to ubikes (university bikes) they are a nice large shop, and probably have the nicest rental selection. my friend rented from boulderbikesmith, the bike was nothing fancy but worked and was in good condition. if you are from somewhere flat, get a triple chainring, you can use it here.
bring your pedals!
Recommended rides (in case you don't have a local connection):
medium: jamestown, via 36, then back via old stage or lee hill (gasp)
long & climbing: lefthand canyon to ward to lyons to the st. vrain canyon (do not miss this road it is great!)
or anything involving the peak to peak highway. it's also nice to drive/bus up to Nederland and ride north on the peak to peak to allenspark (or farther) and back - plenty of climbing up there
flat (well, sortof): carter lake
epic: trail ridge road (start in estes park)
flat: the best north-south flat roads are 63rd, 75th, 95, east county.
weather: bring a lightweight rain jacket, any time you are up in the mountains it could thunderstorm at any time. if you get up and down before 1pm or so you are less likely to get rained on.
have fun in my home town!