Madurai is a major commercial center in South India. The main activity is concentrated around the Meenakshi Temple. These are the places to visit for shopping, and actually many have specific markets for groceries East Masi street, jewelry South Avani Moola street, Electronics Town hall road etc. Madurai is famous for cotton Sungidi Sarees Hand Loom , Brass works, Tanjore Paintings, Handicrafts and antiques. Pudumandapam is an old mall about 500 years old of sorts, where you can find tailors, books, handicrafts and bronze items in quaint shops don't expect brands here. Handloom cotton sarees are available in co-operative stores often a union of several weavers and/or looms like Co-optex.
Beware of touts who may try to sell at higher prices.
ATMs of most nationalized banks are available in the city. There are sufficient numbers of private bank ATMs too. However, you may not find ATMs of international banks like Citi, Barclays etc.
Almost all ATMs accept standard VISA/MASTERCARD/CIRRUS cards.
Credit cards are also accepted in most stores, however they may not be available with small shops. The size of the shop is usually an indicator for this. There may be a nominal service fee at a few shops.
Major banks accept foreign exchange, and you can walk into any branch to enquire. You will also find money exchangers in mid and high range hotels. The area around railway station also has commercial money changers available.