The best hike out of Brooklyn Lake is undoubtedly the Lost Lake Trail (also called Glacier Lakes Trail). This trail runs between Brooklyn Lake and the Lewis Lake Trailhead, and it parallels the northern crest of the Snowy Range down to the gap between the range's two ridges. Along the way it passes at least a half dozen named lakes and several more unnamed lakes and ponds. While it doesn’t appear to climb a lot on the map (the Forest Service map claims 180 feet of vertical gain), the trail meanders up and down across many small ridges and adds several 50-foot hills (in both directions if you are doing this as an out-and-back trail). The trail can be started at either trailhead and done as an out-and-back or a shuttle hike, but the views really make it worth hiking in both directions! Any way it is done, this is a magnificent and awe-inspiring trail that is entertaining from beginning to end.
From Brooklyn Lake the trail climbs up and over a ridge, where you'll have nice views of the lake before dropping down to the two Glacier Lakes at the foot of an apparently permanent small snow field. The trail climbs to the high point of the hike near Lost Lake. From here it is mostly downhill along a ridge that hangs above the very beautiful Telephone Lakes with views all the way down into the Laramie Valley. The last part of the trail is mostly above the tree line and affords great views of Sandy Lake before dropping down to meet the Gap Lakes Trail, Lewis Lake, and the trailhead.