All of these colleges offer mechanical engineering as a major, though you would need to verify whether they are ABET-accredited (something that is very important if your son wants to become an engineer). They also offer some other majors which I thought might interest your son based on the comments in this thread. Depending on where in New York you are, these might be closer or further away, but I tried not to go too far away from NY.
• Penn State Erie, The Behrend College: Only about 3500 students but offers 158 majors. Has a 12:1 student/faculty ratio and offers both engineering as well as technology degrees, and so many others. This is a residential campus (not a commuter one).
• Gannon (PA ): Has mechanical engineering but other possibilities like chain supply management, technical theater/theater design & technology or industrial engineering. About 2900 students here.
• New Jersey Institute of Technology: Has a variety of engineering degrees (including manufacturing, materials, biomedical, etc) but also has engineering technologies, engineering/industrial management, architecture… A bit larger with about 8,000 students.
• Roger Williams (RI): Architecture, Building Construction Management, various engineering fields and technology ones (like industrial technology and manufacturing engineering technology), operations management, etc. About 4200 undergrads.
• Hofstra (NY): Has several majors which seem as though they could be of interest such as entrepreneurship, medical physics, jewelry arts, logistics & supply chain management, various engineerings (industrial, manufacturing, etc). 6,000 undergrads with a 13:1 student/faculty ratio.
• Widener (PA ): Has a major in mechatronics, robotics, and automation engineering as well as other engineering fields like architectural, biomedical, etc. About 2900 undergrads with a 13:1 student/faculty ratio.
• Wilkes (PA ): Offers majors in various engineering fields, engineering/industrial management, entrepreneurship, logistics and supply chain management, and technical theater/theater design technology. About 2100 undergrads with a 13:1 student/teacher ratio.
• York (PA ): Offers majors in medical technology, entrepreneurship, commercial and advertising art, logistics & supply chain management, recording arts technology, as well as several engineering fields. About 3700 undergrads.
• U. of New Haven (CT): medical technology, interior architecture, music technology, and various engineering fields. About 5000 undergrads.
• U. of Hartford (CT): various technologies (architectural, electromechanical, etc), architecture, entrepreneurship, various engineerings (including mechatronics, robotics, and automation). There are 4,000 undergrads with an 8:1 studnt/faculty ratio.
• SUNY Polytechnic (NY): If you’re sure your son wouldn’t be interested in the humanities, this state school offers various technology and engineering majors along with entrepreneurship. About 2100 undergrads attend.
• U. of Scranton (PA ): Offers a major in biophysics, engineering/industrial management, logistics & supply chain management, operations management, and pre-engineering (which I presume is a more moderately paced route to a career in engineering). There are about 3600 undergrads with a 12:1 student/faculty ratio.
• U. of Dayton (OH): Offers majors in various engineering fields, technology fields, entrepreneurship, and operations management. A bit larger with around 8400 undergrads.