Which IIM should I choose amongst Bodh Gaya, Sirmaur, and Jammu?

All the 3 B Schools you mentioned have been established recently and are not very different from each other. My sister is an IIM Jammu pass out so I will mention whatever I know of that particular IIM only.

• It was established in 2016 and initially functioned under IIM Lucknow but now runs as an autonomous school.
• Located in the heart of Jammu city, IIM Jammu gives an edge over other new IIMs because of better connectivity.
• The campus life is a blend of a hectic schedule with tight deadlines that will always keep you on your toes
• Emphasis is also placed on extracurricular activities through sports, cultural and regional events. The Annual Sports Event “Funathon” is conducted to showcase the talents of students in sports.
• Great exposure is provided to students 
• through various Guest Lectures and various events like HR Conclave and CEO Summit
• Being a new IIM, the student-driven culture is at its peak here. You are responsible for solving issues related to the establishment of clubs and committees.

So I think IIM Jammu is probably a good choice.