Dear aspirant, here are some of the best institutes for studying game design in India -

• IIFA Multimedia
• IIFA Lancaster Degree College
• Asian Institute of Design
• National Institute of Design
• ICAT Design & Media College

As per my knowledge IIFA Multimedia college is best for game designing .

Following are some of the careers that a game designer can opt for:

1.Lead designer

2.Content designer

3.Creative director

4.Scriptwriter

5.Video Game Tester

All the best

Hope this helps