Ahmedabad
Ahmedabad was one of the least touristy places I went. It's a city of seven million people or something, but I doubt many people know much about it outside India.
The Sabarmati Ashram, where Mahatma Gandhi lived for many years, and from where he started his salt march, was very peaceful, a delightful place to visit.
They have these amazing "step wells" in Gujarat. I visited two in Ahmedabad. The well itself is reached by a set of large flights of stairs, descending many storeys. Above the flights of stairs, pillars and beams form a set of roofs and passageways.
The highlight of my time here was a day trip to the Modhera sun temple, several hours to the north of Ahmedabad. It's the sort of place where you're glad of people's willingness to assist you, as it required several bus rides and a walk through the village of Modhera to get there. It was an amazing place, with the temple and waiting hall fronted by a clear blue pond (with lots of turtles in). Steps are arranged so that couples can go down together, with the women's steps offset to make them slightly higher than the adjacent men's steps.
On my return, I visited the city's kite museum, which, though not updated for many years, was interesting in showing that Ahmedabad has a culture of kite flying using cutting strings to attack competitor's kites. Just like in "The Kite Runner", if you've read it or seen the film.