Peaks that I like:
ADK (these would be busy on summer weekends)
Gothics, Basin, Haystack (part of the Great Range Trail,
(Miles: 25 Elevation Change: 17,600 feet )
Catskills: Blackhead Range, Cornell and Wittenberg (part of the Long Path, you could probably find some other trails making a loop out of a part of the Long Path (Windham High Peak to Blackheads to Cornell/Wittenberg to Slide) and other trails to connect back from Slide to Windham).