OK, in which case it is totally the wrong time of year to go to the Himalayas unless you are prepared for snow and are into packing tons of thermal underwear!

Try this, as it has a certain logic to the flights:-

Bangalore: Taj West End (2 nights)

Mysore: the Green Hotel (30 nights - because you have to)

Hyderabad: Taj Falaknuma Palace (2 nights)

Delhi: The Leela Palace (1 night)

Agra: The Oberoi Amarvilas (2 nights - travel by car along the new highway)

Jaipur: The Oberoi Rajvilas (3 nights) By car from Agra. Oberoi will transfer.

Jaipur to Jodhpur (always use Jet Airways!): Umaid Bhawan Palace (3 nights).

Jodhpur to Mumbai. Stay 1 nights at Taj Mahal Palace Mumbai then fly home.

Save the rest for your next few trips!