A single famous person was born in Salem: Samuel M. Hopkins
Samuel M. Hopkins was born in 1772. That places their birth before independence. 3 languages have an article about them. Of the bordering towns, Lyme has the longest list: 26, with Morrison Waite at the top.
#1 best knownSamuel M. HopkinsPolitics & Law · 1772–1837
From Wikidata and Wikipedia: people whose birthplace is Salem and whose English Wikipedia article agrees, ranked by how many Wikipedia languages cover each person. People known mainly for crimes, and adult performers, aren’t listed. “The usual town” = everyone born in the towns gathered so far.
Photo credits (8)
Samuel M. Hopkins: Lithograph from painting by John Trumbull, Public domain, Wikimedia Commons
Rachel Robinson: Kingkongphoto & www.celebrity-photos.com from Laurel Maryland, USA, CC BY-SA 2.0, Wikimedia Commons
Morrison Waite: Mathew Benjamin Brady, Public domain, Wikimedia Commons
Lyman Trumbull: Mathew Benjamin Brady / Levin Corbin Handy, Public domain, Wikimedia Commons
Morgan Bulkeley: Harris & Ewing - Photographer, Public domain, Wikimedia Commons