The trout holdover well through the Summer on the BFB, and if the weather cooperates there could be some action, especially in the early AM. The Tricos tend to end early in the Season on the BFB, and as with most freestone streams the insect hatches are sparse this time year. Midges, terrestrials, small caddis may bring a few to the top. With the water low and clear the trout get quite jittery and can be hard to get near (with the exception of a few deep pools).
Your best bet is Blewett Tract and North, but water temperatures can still hit 70+ in some areas. For myself, I give the trout on the BFB a break this time of year unless we have some unusually cool weather like we did in June and July. When the air temps are consistently in the 50's for several nights I might consider a morning on the BFB.
As other have suggested the Pequest or the lower Musky might be better choices because of their limestone characteristics, as well as crossing over into PA where the spring fed limestoners are more abundant.