Here's a list of synth rich locations the testers and I came up with. It's not meant to be a complete and comprehensive list of every location where synths occur, because I bet we forgot some, but it's a fair number of them.

Quest related locations:
Arcjet with Dance
Tradecraft with Deacon
Fort Hagen to get to Kellogg
If you are later in the quest and not going Institute Mass Fusion is a gold mine
If you're going RR Ticon has a bunch, etc.
"defend the checkpoint is good.


Random Locations:
CIT Rotunda
Malden Center
Sandy Coves Convalescent Home in Salem
Federal Surveillance center in the Glowing Sea under the abandoned cabin
Boston Mayoral Shelter
Makhra Fishpacking