Hello,
Congratulations on your score you have chances of getting into top medical colleges of your state. (assuming that usual cutoff is around 560+ for top colleges as you haven't mentioned your state )

You have high chances of getting into following governement medical colleges :-

With 665 NEET score your  NEET AIR Rank will be in top 1248 and your NEET percentile will be around  99.78 - 100

However these information is based on last years cutoff and as cutoff changes everyyear depending on factors like difficulty and number of candidates and current COVID19 situation etc.
To comment on AIIMS is difficult as it will be first time that AIIMS admissions will be through NEET score. However you'll easily get into AIIMS rishikesh, patna at this score.

You can use careers360 college predictor to know the colleges you can get at your NEET score;- https://medicine.careers360.com/neet-college-predictor