This is a smaller bank, with only a few branches in Quito, but one of the few that will exchange traveler's checks. There is a $5 charge for the exchange and they only exchange checks up to $200. The ATM accepts Cirrus and Maestro debit cards and will charge you $1.50 in addition to whatever your home bank charges for international withdrawals.
Branches in Quito:
Av. Naciones Unidas E7-95 y Los Shyris - 593-2-298-2000 (west of Quicentro)
This branch is open from Monday - Friday 08:30 - 16:00 and Saturdays from 09:00-14:00 (but doesn't exchange traveler's checks on Saturdays)
Av. Amazonas 720 y Veintimilla - 593-2-252-1586
Open from Monday - Friday 08:30 - 16:00 and Saturdays from 09:00 - 14:00
Centro Comercial El Bosque (large mall in the north of the city on Occidental)
Monday - Friday 10:00 - 17:00
Saturday: 10:00 - 16:00