Please ignore my friends who like to sit on their high horses at times. There is the possibility for what you are looking for within the Mohonk Preserve.
One easy--to--consider activity is to park at say the West Trapps Lot and walk the undercliff Carriage Road until you get to the start of the Trapps. Here, you can hike/scramble to the top of the cliff and then hike the ridge almost all the way down to the most northern part of the cliff, to the top of a climbing route known as "Casa Emilio" . Here, you can do two rappels with 1 60 meter rope or 1 rappel with 2 60 meter ropes. Then, you can catch the carriage road again and go back south to your car or go north and then wrap around taking the overcliff road back.
This entire excursion would take about, um, maybe 3 hours depending on how quickly you walk and efficiently your party rappells and it would expose you to the unique cliff top environment, with views of the hudson valley and catskills, and a look at the cliff side environment as you are rappelling. On a nice day, it could be quite pleasant..
Casa Emilio is a route that sees only a modest amount of climber traffic, so, you will not likely be interrupting climbers there, but, of course, be courteous to the climbers that you may meet and give them the right of way.
All of the places that I described can be found in any of the Dick Williams guides to climbing at the Mohonk Preserve or in the Todd Swain guide as well.