Mumbai (Bombay), New Delhi, Calcutta are the best to study English in India.
There is no specific course as you will have to take private tutions from experienced Tutors in the said subject.
English language is internationally spoken, read, promulgated for all purposes. It has very many advantages. Yes it will help you for Tofel.
You have not disclosed your country of residence?? it would have helped.
The site 'Incredible India' can give you very many information of India.
The site Tourism in India can also be of advantage for you to assess various locations both for pleasure and historic events.
The best way to study English language on your own is to adopt the following system:
Read an English Daily for atleast one hour, very slowly,pronouncing each and every work legibly. Read the text a bit loud so that you hear what you read/speak.
For any word not familiar refer Dictionary and understand the meaning.
Read some more literature in your spare time, refer Encyclopedia a very informative source.
Try and converse with friends and well wishers in English at the first opportunity. Explain to them that you wish to enhance the subject both in form of speak, read & write.
After 2 months of daily routines as explained above start writing any text - at least one full A4 size page to improve handwritings.