India is BIG and it takes a long time to get between places. To help you manage your trip round India, it's probably best to chunk your journey into two parts, the north and the south. The north is best for visiting all the famous sights of India. It's also great if you want to learn to teach yoga or go on a yoga reteat for a bit. The south is perfect for a bit of beach time (it's also warmer in the south). Goa is the best place to go to party but will also position you close enough to go see some natural sights such as Hampi or to travel down to Kerala and the backwaters afterwards.
Worth noting: Taxis can be dangerous in India, especially for women on their own. To help protect yourself when you get a taxi ask the driver for their phone number, and take a picture of the license plate. All phone numbers in India are registered, so they’ll know that you now have access to all their details and will assume you’ve sent the photo to a friend, so they will get busted if they try anything. I’m not saying this is a foolproof method but it helps. In general try to avoid taxis on your own where possible and especially at night.
Click on each area for more information