My DP is Indian, and we go a couple of times a year.
His family live in Mumbai so we go there, and then travel on. I love Mumbai, lots to see and do - I'd recommend Gateway of India, Haji Ali, Global Vipassana Pagoda, Dhobi Ghat (vast outdoor laundry), Chowpatty Beach at sunset for street food (check water used is bottled "Bisleri"). Muhammad Ali Road will give you every food you can imagine.
From there you can fly anywhere, we tend to go for a few days in Mumbai, then a few days somewhere else, and the same again, before a couple of last days in Bombay and home.
Kerala is a short flight from Mumbai - the backwaters are stunning, and the spice trails are amazing. The tea plantations are beautiful, and the sunsets over the hills are breathtaking.
Goa is also an hour flight, or you can take the train from CST station in Mumbai. It takes 8 hours, goes through SO much stunning scenery, and all meals are provided. The conductor welcomed us onto the train personally with a rose. The seats rotate so you can look out of the window too. We travelled first class last December as we had a wedding in Goa, and it cost us £30 a head for everything. We flew back, again, very cheap.