Are there any banks that offer ATM machines that dispense small denomination bills ($10 or less?)?
Nearly all ATMs have 2 currency trays. Each tray can be stocked with a single denomination. Most banks use $20s in both trays to maximize the total amount they can put in that machine. Some banks stock 1 tray with $20s and the other with $10s. This is usually determined on a machine by machine basis, I doubt ANY bank stocks all their machines with both. I recommend asking your bank if they have any machines stocked with $10s.