As far as I know, scores are not part of the criteria when they select NRI students for medical school in India. You will have to pay a lot of money as a capitation fee and follow that up with yearly tuition fees.
With regards to schools that are good in India and which are definitely very NRI friendly:
1) Kasturba Medical College, Manipal- has a ton of NRI's, you will feel at home here and the culture difference will be much easier to bear. Place is small but plenty of nice places to hang out. Facilites are incredible here and are second to none. Completely air conditioned library with computers for each person, brilliant Anatomy lab and great campus. The biggest downside(atleast from what I have seen) is that though the hospital is nice and has all the recent medical advances available, patient population is a worry and people have told me about lack of exposure to cases in the hospital wards.
2) Sri Ramachandra Medical College, Chennai, Tamil Nadu- same as above. City is bigger than Manipal with more places to visit. Weather sucks though and its always hot and humid. I am not too sure about the facilities here.
3) JSS Medical College, Mysore- Mysore is a lovely place with a lot of history and architecture. The weather is absolutely fantastic and studying becomes that much easier.
They are constructing a new multi speciality hospital with great facilites. The college itself is fine though it does not meet the standard of Manipal. However, it has one thing Manipal does not. It has a great patient load and sees upto 800 patients in the Out patient per day and about 150-200 patients admitted in the wards. You will definitely see a lot of cases and get great clinical exposure. It used to be a private college but now has become autonomous and is currently taking in a lot of foreign students. A lot of Malaysians, Americans and students from the Middle East are coming here.
These are the 3 I am most familiar with. Others like MS Ramaih Bangalore exist though I cant accurately comment on their NRI intake.
Go to the individual website for each college and look around.