I am horrified by how many destinations and hotels many of you factor into your India itinerary for a bare 2 weeks. If it is just a matter of ticking off the locations in a been-there-done-that manner, then I suppose that is up to you, but if you want to experience India properly, then do less and see more.
Since Tata handed over Taj to Mistry and Raymond Bickson was shunted aside for a guy who used to run base-level Hyatts in the US, I and many of my friends feel that the group has lost its way and that standards have fallen quite considerably, both in service and in food.
Taj West End, Bangalore - still the most residential and Colonial of choices, but perhaps not quite as sharp and well maintained as it was. You need to book a suite here, not a room.
The Green Hotel in Mysore? For 3 nights? Why? Mysore is better visited as a day trip from Bangalore. The only real thing to see is the colourful market. It would be more interesting to go to Chennai (used to be Madras) and stay at The Leela there - then you can take a trip to the extraordinary beach temples of Mahabalipuram. Avoid The Green Hotel.
Umaid Bhawan Palace (Taj) Jodhpur - a very beautiful and interesting place, well worth a 3 night stay as it is also an excellent resort.
Rambagh Palace (Taj), Jaipur is well placed to see the sights but I don't understand why you are staying here as well as Sujan's Rajmahal Palace. The other option of course is The Oberoi Rajvilas, which has more of a resort feel. I would not switch hotels - choose one and stick with it. 2 nights in Jaipur is probably enough.
Sherbagh in Ranthanbore is fine for 2 nights, although I personally prefer The Oberoi Vanyavilas.
The Oberoi Amarvilas in Agra for 1 night is a rush, given how much there is to see in Agra (not just the Taj Mahal) and how pleasant the pool is here.
Nadesar Palace in Varanasi is a unique little hideaway with palace style service. If you actually want to see the ghats as well as enjoy the hotel, then 1 night is insufficient. 2 would be better.
Ananda in the Himalayas for 3 nights sounds lovely, doesn't it. Unfortunately, I think it is a spa factory - massages conveyor-belt style. There are much better spas and treatments in other hotels. If you want to relax, then go to Udaipur and stay at The Oberoi Udaivilas on the lake, which has a very pleasant spa. The rooms and suites here are also a lot nicer than at Ananda.
It depends on what time of year you are going. May is the best time for the Himalayas, as it is warm. A more interesting choice would be Wildflower Hall in the Himalayas, which is set in stunning scenery and has a beautiful spa.