Bengaluru is called the Garden City of India and has numerous gardens and lakes. It is also called the Silicon Valley of India, as most of the technology companies have offices here.
Please visit http://en.wikipedia.org/wiki/Bangalore for more information about Bengaluru.
Weather would be warm, may rain a little. I think it would not be more than 80 degrees Fahrenheit though. Some other places you visit may be hotter - especially Delhi, Agra, Rajasthan. But, the hottest months in India are May, June, July. April should be good.
Places to visit near Bangalore
Lal Bagh Botanical Garden
Banneraghatta National Park (to see Tigers in their habitat)
Yoga and ayurveda spas
One day trips
Mysore (Royal Palaces etc)
Belur, Halebid temples (sand stone architecture)
Ooty (hill station)
Hampi (Royal Palaces)
Kerala - Munnar (tea plantations, forest)
Kerala - Alleppy (back waters, canals, ayurveda)
Agra (Taj Mahal)
Jaipur, Jodhpur, Udaipur (Royal Palaces)
Booking trips in India
Makemytrip.com, yatra.com is a good site to book travel within India. You can even book on the airline sites too. I will send you more links separately. All airlines are good - no issues.
Taj Mahal in Agra is usually high on tourists' must-see lists. I think the best way to get to Agra is to fly to Delhi. I can find out and let you know if there is a better way. There are some flights from Bangalore to Agra, but I don't think they fly daily
Pushkar fair in Rajasthan will be really awesome. You should definitely check it out if it is happening during that time.
Using information from my friend Vikram's (thanks dude) wedding blog:
Almost everyone thinking of going to India for the first time is also thinking of visiting the Taj Mahal, which is in Agra.
Starting with Delhi first - I'm not as conscientious as Carina, and am going to use Wikipedia as my crutch. The Delhi page is very detailed.
* Weather-wise, Delhi will be hot when you arrive
* I kid you not, you are in for an epicurean journey the likes of which you may have never before experienced. Definitely try out:
o Kareem's. There are two locations, one in Old Delhi near the Jama Masjid, and one closer to where most of us will be staying. For those familiar with Shalimar in the bay area..... I'm really sorry, but after Kareem's, you'll weep with joy, and angels will sing over you. Shalimar will never again taste as good
o Salim's, if you are staying near the Greater Kailash regions in New Delhi. Really good Tandoori Chicken!
o Sagar Ratna for South Indian food. They are a chain, with restaurants everywhere
o You must try out Indian Chinese food. You could also wait till you get to Mussoorie, to try out this amazing cuisine. In Mussoorie, I'd recommend the Tavern restaurant
* There are a lot of places to see in Delhi. A small sampling -
o The IIT campus. Hey, I have to talk about my old school :)
o The Jama Masjid - Asia's largest mosque
o The Red Fort
o Humayun's Tomb (Humayun was one of the mughal emperors, and had a good eye for architecture and the arts)
o The Raj Ghat - memorial to Mahatma Gandhi
To see the Taj Mahal, and Agra, you should set aside one full day. I'd recommend renting a cab for the day
There are quite a few buses and trains to Agra too!