As usual, a great source of for more information about Beaver Creek is the CNY Hiking page and the DEC page devoted to the forest. CNY Hiking also has a page about the Brookfield Swamp Loop, a convenient loop that'll take you through all the best parts of the forest.
As the pictures will show, I hiked the loop in the fall. The foliage by late September was amazing. The trails were clean and easy to follow and the CNY Hiking page describing the loop is mostly accurate.