Both CSE at MNNIT and Mechanics at Mechanics IIT Mandi is highly esteemed programs. The choice of the institute depends on your personal interests and career prospects. The branch you choose is more crucial than the institute from which you pursue it. So make sure your passion is the driving factor in choosing your branch. 

If you have an interest in either CS or Mechanics go for them respectively. When you pursue a stream of your choice, the chances of you becoming successful increase as you are motivated for a long time. But if you are not certain about your inclination, then my suggestion is CSE at MNNIT. CS program is well-regarded and is one of the highest-placed branches in MNNIT. 

Personally, I would never recommend anyone to go for IIT Mandi as it is a relatively newer college than MNNIT because of which it lacks in terms of alumni and industrial ties. Additionally, the faculty of IIT Mandi is not at par with old colleges. The only reason one can join IIT Mandi is when they are adamant about the IIT tag. Else, MNIT CS will not disappoint you.

Ultimately, it is important to research both programs and consider factors such as location, campus culture, course offerings, and job prospects before making a decision. 

At IIST, most of the students are inclined towards ISRO. Even if you are interested in it, you might lose interest in the latter half of your bachelor's and then may regret your decision because IIST has very limited career options. That being said, look for an institute that caters to a variety of career prospects so that your options aren't limited. 

Considering the new IITs, both IIT Hyderabad and IIT Patna show promising results. I have a friend in IIT Patna and after a long conversation with him, I realized it has a plethora of opportunities both in terms of placements as well as higher education.

The placement scenario at IIT Patna is great and has been improving every year. 

•  IIT Patna has all big shot companies for placements like Microsoft, Amazon, Cisco, Samsung R&D, UHG, Practo, Yodlee, Flipkart, Arista Networks, Texas Instruments, Finisar, Tata Motors, L&T, Mahindra & Mahindra, Bank of America, etc.
• For those who prefer a stable job, many PSUs like Indian Oil, Bharat Petroleum, HPCL, DRDO, Coal India, etc come for recruitment here. 
• If you are among the top 1% of your batch you can get placed in companies like Google and Facebook, the pay scale of which is the highest you can get.
• The small batch size increases the probability of getting more placements in top companies than old IITs with huge batch sizes. 

Prospects for higher education:

Only after you become a part of the IIT family will you understand the true essence of the IIT tag that opens infinite doors of opportunities for you be it higher education or internships.

• My friend secured an internship in Germany only because he had ties with the IIT brand they said.
• Out of 37, 4 had the chance to do foreign internships which is a lot
• The students of his batch even went to top universities like Stanford, CalTech, etc. for their summer internships.
• Every year many students get qualified for the DAAD WISE scholarship in Germany, the Charpak scholarship for internships in France, and the MITACS in Canada, etc.
• As for MS and PhDs, around 18 out of 150 students pursued their higher education in US and Europe. Today they are placed in the top companies like Intel Corporation, Texas Instruments, Intersil Corporation, etc. in their respective countries. 

Having covered all career prospects, I will leave it to you to decide which institute to join.