Understand
The language spoken by people in Vadodara varies, but almost everyone speaks Gujarati and Hindi. Marathi community is also on a large scale in the city. Most young people speak passable English, and in certain areas you will meet people that are fluent in English. Alkapuri is heavily frequented by NRI's non-resident Indians and has western restaurants Pizza Hut, McDonald's, Subway, CCD, Barista, Barbeque Nation etc., stores Adidas, Nike, Metro, etc., etc. This area is frequented by highly affluent individuals and you can generally find English speaking people on a large scale.
Recently the city has been attracting many International IT Companies to invest in the area to set up operational hubs, including L&T, Collabera, and TCS. Many people from IT centers in India like Bangalore prefer working here because of the simple life, but with all resources like schools, water and electricity.
More information at the Vadodara's official page by Gujarat Tourism