There were a lot of multi-sector flights in the 60s & 70s so 707s will have operated some very short flights. I think (but stand to be corrected) that TWA operated between Los Angeles & Long Beach. I'm pretty certain that Pan Am operated 707s between Miami & Nassau, and Kingston & Montego Bay (maybe without traffic rights though). More recently Virgin & BA have operated 747s between Carribean iaslands.
There were a lot of flights between Miami & Ft Lauderdale in the 70s but all the ones I have looked at were 727s or DC9s. I suspect that some may have been operated by 707 or DC8.