Visit Pi shoppi for wide collections of all types of bags.........I bought a fancy handbag at Pi shoppi OMR branch..... It is not only fancy but of good quality....I bought an imported leather handbag for my mom also... It was very stylish and awesome. They have branches at Velachery and T.nagar. Hope ur search may end there. Reach them 044-43000000
There is a shop called Shabnam in Spencers on the first floor. I think 1st phase. He has a decent collection not very fancy ones, but quality is good and also reasonable. Other than this, there are lots of shops in Spencers itself
While I was resident of Chennai earlier, I always buy my hand bags from Witco. They had lovely bags those days. Even now they have. But now Hi-design has good options, but are expensive. Their outlets are available in many shopping malls in Chennai. Also many Branded shops have outlets in shopping malls in Chennai now viz. LV, Prada, Coach, Hermes etc...... the price goes between Rs. 3 to 8K approx. Regards Shanti