This write-up is element of our most recent unique part on Museums, which focuses on new artists, new audiences and new means of pondering about exhibitions. MONTICELLO, N.Y. — Like its sister towns nestled nearby in the Catskill Mountains, signals are everywhere you go that the cultural and financial heydays of this seat of Sullivan County have been deep in the past. Amid the nods to modern day existence in the city center — barbershops, a sporting activities bar, a pizza parlor and other informal eateries — storefronts in buildings from the 1800s sit empty and inns from the borscht belt growth of the 1950s are nonetheless boarded up. A…