From what I've seen, they close the road starting at the highest elevations, so a portion of the road will likely still be open. And, assuming the road is closed at the top, you should be able to do a partial circle trip: leave Estes Park on Hwy 36 and take TRR west as far as it is open. When you come back down, turn left onto Fall River Road, which also will bring you back into Estes. From Estes, take Peak-to-Peak Highway (actually several Highways: 7, 72, 119) down to I-70. PtP also has some beautiful mountain vistas on a clear day. At Blackhawk to get to I-70, you can turn right to drive through BH and Central City to get on the Central City Parkway (which also has nice views) or you can go straight to Hwy 6, which takes you through a picturesque canyon and along a small river (Clear Creek), which ever you prefer. Google Nederland, Central City, and Blackhawk to see if the shops, restaurants, and casinos (non-smoking) are of interest to you.

You can also access a portion of TRR from the West, going north from Winter Park. Even if closed at the top, I would not be surprised if more than 50% of TRR was still open at that time.

If you look back at similar threads, you will see a lot of warnings about elevation sickness that you should also heed. From CPH, you are gaining about 5k (feet) in altitude to get to Denver/Boulder, another 2k+ to Estes, and then possibly another 3k+ into RMNP, depending on where the road is closed. If not closed, I think the top elevation on the road is more than 12k feet. So drinking lots of water is important, and take a day at 5k if you can to see Boulder, Fort Collins, Denver, etc., as that would probably help you acclimate a great deal also.