What is Manipal University Jaipur’s reputation?

Ashish pointed it rightly, It is an upcoming branch and having backing of MU,Manipal and run and owned by the Manipal group itself unlike Sikkim (It is a joint venture between govt and manipal group).
Faculty is good to excellent. Also college is growing very rapidly and Manipal group is burning midnight oil. Placements this year was mind blowing with an excellent infrastructure.
It has a very bright future. Coming years it will be one of the best universities of the country.
Go for MUJ and I am sure you wont regret.