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Hi Daksh,
If you don't have home-sickness phobia and are absolutely fine to pursue courses in other states, then I would suggest you to appear for as many states as possible. Better opt for those states where there are companies of your core stream. For example, pursuing mechanical engineering in Bangalore is not a good choice as the city is dominated by the IT industry. Similarly, studying IT in West Bengal isn't a good choice as the state doesn't have too many IT companies.
If there are more companies related to the stream you're studying, the chances of on-campus placement increases. Else, you'll have to depend on off-campus placement which is generally tougher and more competitive.
Further, every state in India has its own list of good colleges. Just because of geographical conditions, I don't consider it wise to skip a better college. I hope it clarifies.
As you haven't stated the stream in which you wish to pursue engineering, I won't be able to suggest you any recommendations.
I hope it helps. If so, kindly upvote this answer. If you have any further questions, kindly revert.

In terms of job prospects, both are good. I would list the pros and cons of both.
Suppose you consider medicine as your career:
Pros:
Better prestige and respect.
You can be your own boss if you open your own clinic/hospital.
You'll be able to serve people.
Money (However, exceptions are there in comparison to software career).
Cons:
Becoming a doctor means you need to study for almost 8-9 years (considering you go for Masters after completing your Bachelors).
Moreover, getting into Masters is not that easy.
Cost of studying (depends on the institute you take admission) and then cost of clinic/hospital.
Tremendous responsibilities.
Suppose you consider software development as your career:
Pros:
Less responsibilities at least in the initial years.
Less years of studying.
Comfortable working conditions. No mid-night emergency calls.
Work from home (Depends on the company you work for).
Cons:
Prestige and respect might be less as compared to a doctor.
Less money as compared to a doctor (again it can vary and exceptions are always there).
Global competition and outsourcing. Layoffs.
Coding can get boring after initial few years.