Hello student 
You have not mentioned which category you belong to nor the state. With a score of 420 in neet, if your category is general, then the possibilities of getting a seat in the government medical colleges is less when comparing the results of previous years. It also depends on the state you choose. For example, With this score, you have chances of procuring a seat in the government medical colleges of Uttar Pradesh while it is not so in the case of states like Tamilnadu for which the scores are extremely high. Also, one thing to keep in mind is that scores and ranks vary each year with difficulty level of the question paper and availability of seats. However you can predict the colleges which you are likely to get using the given link
http://medicine.careers360.com/neet-college-predictor
Good luck

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