Im not sure if by estes park you mean your staying in the small town full of candy shops and tourist attractions or if your using that as the common colorado slang for going to rocky mountain national park. If your going to the park, be aware it is very difficult to just show up and get in. That time of year more people than the limit show up everyday. Often times the line to get in is dependant on people leaving, and can be waiting several hours more than one day before you get in. DEFFINITELY RESERVE A PARK ENTRY. And june first is early for high altitude. Old falls road might not be open for the season. Sometimes 130 in wyoming is not open. Most of the dirt roads off of 130 in wyoming have snow drifts well into july.
With the disclaimers out of the way, if you dont mind some driving you can go see hot springs in saratoga wy, fish the north platte. If you dont mind driving another day, the gates of lodore, the dinosaur national monument, flaming gorge, green river, all of the roosevelt national forest around rocky mountain national park.