Some of my friends studied at MNNIT, so I might be able to answer your question. It is suggested that you choose Mechanical at MNNIT Allahabad rather than Civil at NIT Trichy.

Your branch of choice is more important than your college preference. In terms of opportunities, Mechanical Engineering has a slight advantage over Civil Engineering

Mechanical at MNNIT Allahabad has a consistent placement record. Mechanical students receive more job offers than Civil Engineering graduates. PSUs often choose Mechanical Engineering graduates.

Finally, everything depends on your interest and choice. So think wisely and then make any decision, because this will be the building blocks of your career.

I have friends pursuing courses you mentioned above at either institute. Based on the discussion I have with them, here is what should be best for you,

1. The institutes can be considered quite equivalent to one another, but BITS Goa has an upper hand. 
2. M.Sc at BITS Goa can be specialized following the first year, during which you will be allocated a B.E course depending upon your CGPA. 
3. With a 6 CGPA, you can get Mechanical Engineering, which is quite an easy job. In contrast, it is better than ICE.
4. However, if your scores are high enough then you might get a seat in CSE. 
5. By the end of 5 years, you will be receiving a B.E and an M.Sc degree, which is nonetheless a smarter choice. 

However, the fees at BITS Goa are quite a lot. 

CSE/ IT is a preferred branch but the colleges offering these streams need to be compared on the basis of the following parameters Fees, Seats, Placements, Number of companies visiting the campus, and Cut-off.

The aforesaid parameters can be justified in detail below for both CS and IT separately.

Course Fees:

• NIT Surathkal has a fee range of Rs. 4.94 Lakh for computer science/ information technology

• NIT Trichy provides the course at Rs. 5.24 Lakh.

• DTU provides both courses within a primary range of Rs. 7.81 Lakh.

• BITS Hyderabad provides a computer science course at Rs. 15.66 Lakh

• IIIT Allahabad has a fee range of Rs. 15.66 Lakh.

Eligibility & Cut Off scores:

The eligibility for CS/IT at all the institutes is set as 10+2 with a minimum of 60% and JEE Mains score except for BITS Hyderabad which accepts BITSAT scores for admission. The cut-off score varies accordingly.

Placements:

• NIT Surathkal offers 100% placements with a record of an entire batch of 98 students. Primary recruiters are Capgemini, Genpact, Samsung R&D, Wipro Ltd., and CitiBank Ltd.

• NIT Trichy offers 95% placements in the sector of technology and operations. The top recruiters are HCL, Genpact, Wipro, Zoho, and Tech Mahindra.

• DTU offered 433 job offers in core engineering and technology firms focusing around 131 IT firms. 158 job offers were made along-with 122 students placed successfully.

• For BITS Hyderabad 120 companies participated from the IT sector, the majority of them were leading players like Adobe, Google, Microsoft, and Linkedin.

The other factor that is to be concerned is definitely the ranking and reputation of colleges in the marketspace. Both the NIT’s are exemplary performers in the field of engineering. IIIT focuses primarily on information technology. BITS in comparison to all is a private institute that can be a little behind in the race compared to major government institutions.

NIT, Srinagar, and NIT, Trichy both are government colleges that have been awarded NAAC grade A. NIT, Srinagar has been ranked 67 by NIRF,2020.

Both NITs offer BTech courses for CSE and Chemical Engineering and both the institute take admission through JEE Main. Some of the key information about the CSE program at NIT Srinagar and Chemical Engineering at NIT Trichy is as follows.

Facilities:

NIT, Srinagar:

Many facilities are available on campus like high-speed Wi-Fi, hostel (shared by 4-5 people), Library, medical facilities, etc.

• The labs for students are well equipped with the latest technology and tools.

• The library on the campus is well stacked with the latest publications, journals, and books.

NIT, Trichy:

The campus of NIT, Trichy is spread over 80 acres with various facilities on campus like a library with the latest books and journals, indoor and outdoor games, swimming pool, medical facilities, Wi-Fi, cafeteria with north Indian and south Indian food, etc.

Faculty and Academics:

NIT, Srinagar:

• The faculty is well qualified, reputed, and has experience in diverse fields.

• Teachers are supportive and helpful. They encourage students to take up internships to gain practical exposure.

• Various industrial visits are organized for the students. Seminars and workshops are also organized.

• Tech Fests are also organized annually.

NIT, Trichy

• Teachers at the department of Chemical engineering at NIT, Trichy are all highly qualified Ph.D. holders.

• Industrial visits for students are common. A fest called 'PRAGYAN' is organized which is very famous among students and well attended.

• Seminars and workshops are also conducted frequently.

Placements:

NIT, Srinagar:

• The placement opportunities for CSE, Srinagar are good. Many companies like TCS, Wipro, MU sigma hire students.

• Companies hire students who perform well in interviews and have also done well in academics.

• The average salary offered is around 6 LPA.

• For CSE the placement average is around 100% according to the 2020 placement drive.

• The highest CTC received by the students in 2020 was 19 LPA.

NIT, Trichy:

• Teachers at NIT, Trichy have good contacts with many companies. Companies like Google, Axis Bank, Nestle, L&T, ONGC visit to hire students.

• The average salary offered is around 8 LPA.

On-campus placements are higher at NIT, Trichy compared to NIT, Srinagar.

Both the colleges are good and have their own advantages. The choice of college depends on the individual's feasibility and goals.

NIT Trichy would be a better choice than IIT Bhubaneswar for Metallurgy because of the following reasons.

• The placements are better for in ECE than in Metallurgy.
• If students fail to get core placement in NIT Trichy, they can still try for top-notch coding and management companies recruiting from the ECE department.
• There are numerous Technical clubs for first years students who are passionate about Electronics.
• NIT Trichy has lower academic fees than IIT Bhubaneswar. But it may vary for different courses. The course fee of B.Tech in NIT is 72,100 whereas in IIT Bhubaneswar it is 1.4 lakh.
• In terms of quality of infrastructure and social life, NIT Trichy is better than IIT Bhubaneswar as it is much older.
• NIT Trichy ECE in 2019 has undergraduate placement of 95% and IIT Bhubaneswar Metallurgy has 90% placement in 2019.