You can take up to 25K INR in cash at the airports (after converting your USD to INR at an exchange kiosk).
And yes, I agree you should send the money to your NRE account in India via online wire transfer. There are many services available at different rates. If you need to send money fast, the charges/fees will be higher (like through an agency like Western Union). If you have time on your hands, the charges will be less and you will get better conversion rate (like through a bank).
I’ve written a detailed article on this here.