My knowledge is limited to IIT Patna as my brother was a student of the same and thus my answer talks about that particular institute only. Firstly, judging an IIT on the basis of its location is not logical. What matters is the job opportunities and facilities it has to offer. In that sense, IIT Patna will definitely serve you well. 

IIT Patna offers one of the best UG EE Courses. For an undergraduate student, EE is one of the most challenging branches. But the plethora of opportunities it has to offer makes it a more lucrative branch too. IIT Patna EE branch includes courses from both Electrical and Electronics leaving you to decide on which field to pursue.

If you are inclined to CS and coding stuff, you can do it despite being in the EE department. IIT Patna has one of the best coders, a senior of the EE Branch who cleared Google Code Jam and was also part of this year’s ACM-ICPC Team which qualified for World Finals and Secured 56 Rank. Another senior cleared GSoC which is quite an achievement.

If you are a research enthusiast and want to go for a Master's, then IIT Patna is the best place. Its highly supportive professors help you in every way. The seniors are helpful and guide you in making the wisest decisions.

It’s best to talk to the students of all the institutes you mentioned and then decide.

Pursuing CSE from any Tier-1 college will be very beneficial for your career as it’s one of the most coveted branches today. 

NIT Jalandhar all three branches CSE, IT, and ECE are the top ones with excellent placements. These branches offer excellent job opportunities irrespective of the fact that you know how to code or not. Students of these branches are placed in companies like Microsoft, Amazon, Samsung, Flipkart, Paytm, and even Google. Additionally, a 6-month internship program in the 8th semester is offered wherein you can intern in any company (off-campus or on-campus) and earn while being a student.

So, you can put your worries to rest if you are only concerned about placements.

When deciding on a branch of engineering, it is important to consider the long-term prospects of the field and the policies of the university offering it. Here are some points to keep in mind while choosing a stream:

• While some may argue that mechanical engineering is better than newer branches, it is important to keep in mind that every branch of engineering has its own set of advantages and opportunities.
• Thapar University is a private institution that may prioritize profits over student interests. As such, it is important to consider the policies they set in place to make money.
• Certain branches of engineering, such as mechatronics and robotics, may be kept to earn more profits, as they may charge an extra 10k in addition to other expenses associated with these streams.
• It is also important to consider the job prospects in your chosen field. Some companies may not offer jobs to those in certain branches of engineering, which can impact your career prospects.
• It is advisable to do thorough research before choosing a branch of engineering. Speaking with current students and alumni can provide valuable insight into the field and the university.
• One should also keep in mind that switching branches may be an option. If, like a friend of the speaker, you find that your chosen branch is not a good fit for you, it may be possible to switch to another branch, such as computer engineering.

In conclusion, choosing a branch of engineering should be a well-thought-out decision, taking into consideration the long-term prospects, policies of the university, and job opportunities in the field. Doing proper research can help ensure that you make an informed decision that is right for you.