Would second that Indian Peaks is both beautiful and crowded- I’ve still found good luck on weekday trips there (see a good amount of people, but still plenty of solitude if you want it), but I avoid weekends completely.
A farther drive but much less crowded is the Neota Wilderness to the north (or you could start in the park and hike out, would avoid backpacking permit but not sure about car-overnight regulations); another option could be driving over Trail Ridge Road (closed now, should be open in mid July) and doing Indian Peaks from the West- much more parking spots.
If you are willing to drive more than a few hours from Estes, your options open up a lot. You could do a section of the Colorado trail (Breckenridge to Copper/vice versa is easy logistically as you can leave a car and take the free Bustang, then hike back to your car), or the Lost Creek Wilderness Loop, both relatively popular, or explore the Medicne Bow-Routt National Forest for more solitude.
Don’t know where you’re coming from or your familiarity with CO, but one of the great joys I’ve found living out here is a long road trip to a trailhead is filled with breathtaking beauty along the way. I’m local, PM me if you want to talk more details or if I could help shuttling.
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