The Mount Beacon fire tower trail (Or Casino Trail as it is called on the official Hudson Highlands Trail Map) is a very popular and steep switch back trail that leads you to an initial overlook over the Hudson River, the city of Beacon and across the river to Newburgh and beyond. Once the first overlook is reached (The turnaround point for many), the trail continues, flat for a bit and then more uphill, to the fire tower which can be seen from the initial lookout by looking south east. The trail follows red trail markers until about a tenth of a mile from the fire tower, at which point you traverse a rock scramble on the white "breakneck ridge" trail to get to the fire tower. This route begins in the parking lot and ends as you touch the fire tower. Runners be warned though, on a beautiful weekend day this trail can be flooded with visitors hiking single file up the switchbacks to get to the initial overlook. If visited on a weekday or early in the morning though, there is plenty of space to maneuver and run.
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Here is a Strava segment for this route, looks like the fastest time is around 22:16 or so.