Last year in mid-May, we hiked up to a few amazing alpine lakes in Colorado. These were all spectacular and really enjoyable. First two were suggested by a friend who's a longtime resident of Estes Park, and who hiked with me and my partner.
One consideration is you may need a timed parking pass -- do read up on the current situation with parking in RMNP. I was getting them online in the late afternoon when a bunch were released, for use the next day. Alternatively, get to a lot before a pass is needed (6am, IIRC).
Here are some AllTrails links. First two are off of Rt 7 south of Estes Park:
Sandbeach Lake - wonderful, felt remote, with huge mountains around
Chasm Lake - awesome rock walls above the lake - caution: there was a potentially dangerous snow field crossing, microspikes absolutely needed especially as it gets melty in the afternoon. This feature is mentioned in some of the reviews here.
This one is a circuit of several lakes, southwest of Estes. Bear Lake is right there too at the parking lot:
Nymph, Dream, Emerald, Haiyaha Lakes - warning: extremely touristy, go very early like before 6am to avoid the crowds. The first part of the path is paved, but as you go up it feels wilder, and the views were great.
Have a great time!