Hi Shikhar
NIT Trichy, Warangal, Surathkal are a much more reputed institutions than MNIT Allahabad. If u just wanna stay in Allahabad because its close to your dwelling place than i don't think u'll be making a good choice.  
NIT Trichy and warangal have good faculties and a good placement record. Getting into these will surely fetch you a better placement. But do balance ur department choice with the college. If getting into NIT allahabad gets u the branch of your choice , go for it.
As per your rank chemical or mechanical engg. in NIT Trichy wud be the best choice. You can also consider Electrical and Electronics in NIT Surathkal, if u cud get it. Else other branches are available to you as per ur choice. 
I would suggest you not to limit your future prospects just because u need to move away from home. Living in hostels is also fun and nothing to be feared about. You'll adjust in less than a week. If u need to see more detailed opening and closing ranks for the AIEEE , then please follow the linkwww.askiitians.com/aieee-counselling/aieee-engineering-counsellings.aspx.
best of luck