Clothing choices depend on the job. Young Indian women working for international companies or in international offices often wear western suits. But unless there is a dress code that specifically requires everyone to wear Western clothes, everyone is welcome to wear the same types of clothes they would use in the same type of office back home. Thus, in some offices, you will see western women in suits and Indian women in fancy salwar kameezes or saris. You may even see a few western women in fancy salwar kameezes. In Indian offices, the dress is mostly Indian, of course.

For just going around town, you wouldn’t want to wear a suit because it’s too hot (and a skirt suit would show too much leg for walking around town). Just wear what you would for similar events and purposes back home. In the malls, on the streets, on the beaches, Indian women wear saris and salwar kameezes, as do a few western women. Certainly for Indian cultural events, you will want to have your best sari.

If you need a specific answer: Jeans with shirts / blouses / t-shirts are ones I see most commonly. They wear all other dresses you can imagine of.

Don’t know what you mean by ‘local markets’.