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With a NEET UG score of 666 and an All India Rank (AIR) of 14,583 under the OBC category, you have a good chance of securing a seat in several medical colleges across India. Based on previous years' data, the expected cut-off ranks for OBC candidates in various government medical colleges range widely, typically from about 250 to 4,000 for top-tier institutions.

Given your rank, you may be eligible for admission into several government medical colleges. However, your chances will also depend on the specific quotas and availability of seats during the counselling rounds. Here are some colleges you might consider:

1. Maulana Azad Medical College, New Delhi - historically, the cut-off for OBC candidates can go up to around 397.
2. Seth G.S. Medical College, Mumbai - previous years show cut-offs that may allow admission around your rank.
3. SMS Medical College, Jaipur - often has cut-offs that can be accessed with ranks close to yours.

Keep in mind that the final decision will depend on the specifics of the counselling process, including the availability of seats and the competition in the current admission cycle. You should also check for any updates related to the NEET counselling process for the current year to confirm your eligibility and options.