We are not certain we know of all his accounts.
Be sure to take letters of executor for his estate with you to each bank for which you can find any receipts among his papers. When I did my father’s estate I had to contact banks in VA where he lived previous to retiring, to find all the trails for accounts. I still had a key that looked like a bus station locker key which I never did connect to a source.
Then, yes, call every bank in 100 mile radius. Tell them that he died, that you think he had accounts there, and ask them to confirm whether or not he did. Also, as another FReeper suggested, check the state’s abandoned property records.
As my parents aged and were slipping into dementia, wifey and I were fortunate enough to received their permission to begin handling their affairs and finances.
It sure made it easier on us after their deaths.