there are various universities which are offering M.Tech and M.E in mechanicals Engineering like IIT,NIT and many other university like DCE which is now DTU, BITS, Anna university, PTU, and many more for more information you can visit the following link
The list of universities offering B.Tech in Mechanical engineering through correspondence in India are -Andhra UniversityJNTUKarnataka Open UniversityRVD UniversityYashwantrao Chavan Open University
Indian school of Mines DHANBAD
Sant Longowal Institute of Engineering and Technology, Longowal, Punjab
defence institute of advance technology pune offering masters in mechanical weapon
The list of universities offering engineering courses through distance learning are -Andhra UniversityIGNOUJNTUKarnataka State Open UniversityRajasthan Vidyapeeth UniversitySRM UniversityThapar UniversityYashwantrao Chavan Maharashtra Open University
Mechanical engg has best placement in India.
Anna University is one of the most reputed universities in India Offering engineering courses in various majors meeting current global technical and industrial development.
number 11 at present among private engineering universities
sams
Environmental engineering is a very good field to get in to. It is very lucrative and rewarding.
bharthiar university in coimbatore, bharathidasan university trichy
For a start you can refer the link -[http: //study.taaza.com/study/direct-phd-after-b-tech-mechanical]for colleges in India. IITG is highly recommended.also if you have given your GRE and have a good score, there are many universities which you can approach.http://study.taaza.com/study/direct-phd-after-b-tech-mechanicalis an example for direct PhD in ME.