Tell me when is the correct time to write GRE and TOEFL. I’ll finish my BE in JUNE. Any institutes in Bangalor

I am going to finish my BE (Bachelor of engineering) in June-July. When do u suggest me to write both GRE and TOEFL?
When should i apply for writing them? I can immediately join in
a good institute for coaching to get a good score. Please suggest a good institute in BANGALORE which offers both courses(GRE,TOEFL) daily .Tell me their website for details if any. What r the good universities in US? I dont prefer CANADA. Also give me all the information u know regarding this whole process right from writing the exams till getting a seat in a good university and life thereafter.