If you are spending 1/2 your time in boulder, you can keep yourself busy on the front range drainages. The front range has multiple parallel drainages that are about 20-30 miles apart and almost all of them have good class IV+ on them. Check out Bailey (V-), blackrock on clear creek (V-), boulder creek (IV/IV+), big thompson (IV+ if dam is releasing), south boulder creek (IV+ with some V).
On the road trip, clear creek of the ark (V-), castle creek into slaughterhouse (IV+ near aspen), and the upper animas (V-, durango) would be a great road trip. If you head down through crested butte you might want to check out the upper east, the slate or daisy creek. Get your pick list of runs and plan your route out using an online map to minimize driving times.
A great online resource is Eddy Flower
Lots of info for all of the runs I listed. Another good source would be to search mountainbuzz (upper right hand) for previous requests. There have been several over the past couple of years.
I wouldn't recommend Gore in june for IV+/V- paddling. Its typically high during June and I haven't heard of any IV+/V- boaters paddling it, mainly the class V crew.
You will need to check flows when you get here to see whats running. June is a good time to come and you should have lots of options. Do your research, get a good guidebook, plan out the trip, and post back here with your itinerary. There are some runs that look good on paper that I would skip (tenmile creek, alto alto).