Boston Private Bank & Trust Company 1666 Massachusetts Ave, Lexington, MA02420 Boston Private Bank & Trust Company has been in business since 1987. This branch is located on Mass Ave across from…More the Post Office in Lexington Center. It is a specialized bank, dealing primarily with high net worth individuals, as well as business clients of all sizes. While the bank has ATM's and handles checking accounts, Money Markets, CD's and home mortgages, it does not issue money orders or credit cards and it does not have safe deposit boxes. They work very closely with their clients, keeping them abreast of current market conditions and offering advice on how best to manage their funds.