All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If it is possible to cash the cheque from an Islamic bank or an institution that abides by Islamic rules and offers those services, then one should not go to a bank that deals with Riba (interest and/or usury) because dealing with such a bank means helping it continue and grow.
However, if the bank which deals with Riba is itself the bank which issued the cheque and the owner of the cheque deserves the amount stated in the cheque and he was directed to this bank to take his right, then it is permissible for him to cash it from the bank that deals with Riba, as by doing so, he is neither considered as consuming Riba, nor giving it to others to consume, nor helping in it. Rather, it is like someone owes you an amount of money and he referred you to another person who owes him money and who consumes Riba to take your debt from him, then this referral is correct. For more benefit, please refer to Fatwa 94389.
Allaah Knows best.