Hi Nellie,
Since ur flying out of Bangalore it would be better to spend half the time in the North and then move on to South before catching ur flight out of India. The weather would be perfect for u to explore the whole of India.
North India I will advise you to not to miss Rajasthan ( cities like Jaipur, Udaipur, Ajmer, Pushkar, Jodhpur, Bikaner, Jaisalmer which have lovely palaces and forts) . Also the places in North India which are not to be missed are Agra(Taj Mahal), Varanasi, Delhi, Amritsar( u can go upto the international border of India-Pakistan).
If u like the hills then head straight to Himachal pradesh which has beautiful hill stations like shimla, Manali, solang valley, Dharamshala, Mc Leodganj. The road to Leh-LAddakh would be closed due to heavy snow, but if u still want to visit it, u can catch a flight from Delhi.
Once north india is finished u can move to the South India
Travel down to Mumbai (which has numerous excursions available) and visit Goa which is an overnight journey from mumbai. Goa is famous for the beaches and typical Goan cuisine.
Then moving on to South india, which is famous for the beautiful temples,places not to be missed are Madurai, Mysore, Chennai, Tanjore, Hampi. What i recommend the most is to visit the State of KERALA, which is called the God's own country. This state has a number of backwater cruises to suit every budget. In Kerala, the traingle of Munnar(hill station), Thekkady(wild life reserve) and Alleppy(Centre of backwater activites) are not to be missed.
Regarding internal transportation, where long distances are to be covered, it would be preferable to take the ariel route. Some of the domestic airlines are:
www.jetairways.com
www.indian-airlines.nic.in
www.flykingfisher.com
www.spicejet.com
www.goair.in
www.goindigo.in
U can prefer train/bus for shorter distances. Train tickets can also be booked upto 90 days in advance at www.irctc.co.in
Regarding accommodation, India has a host of options from budget to expensive ones and the rate depends on the season when ur visiting.
Do let me know if u need any specific information
Cheers
Arif