Geico insurance is ripping me off?

I am licensed in FL and not in NM. This is offered as a general discussion of the insurance issues that you raise and not as legal advice. No attorney-client relationship is created or intended.
It is difficult to answer your question with certainty without seeing your policy. Increasingly, the collision coverage of policies are being handled in a "managed care" sort of way (much like health insurance) such that an insurer has a list of "preferred providers" to which it refers you. That may be why they sent you to the dentless repair facility initially.
You are generally entitled to have the car put back in the condition it was in prior to the collision. The most direct thing to do would be to take the car to another legitimate repair facility and get a complete estimate. Yes, you may have to pay for it, but many facilities will refund that fee (or work it into the estimate) if you ultimately have them do the work.
Keep in mind that your comprehensive coverage deductibe (which would apply to hail damage) may or may not be in the same amount as the deductible on your collision coverage.

Greetings:
I do not practice in New Mexico.
The Consumer Relations Insurance Bureau offers assistance to consumers seeking to resolve disputes and complaints with licensed New Mexico Insurance Companies. Go to:
http://www.nmprc.state.nm.us/complaints.htm
I hope you find it helpful.
Best regards,
George P. Conway
THESE COMMENTS ARE NOT LEGAL ADVICE. They are provided for informational purposes only. Actual legal advice can only be provided after consultation by an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation

Generally, unless your insurance policy says otherwise, you have the right to select the repair facility at which your vehicle is fixed. It sounds like the company was trying to rush you and force you into accepting an unfair settlement. I suggest that you get another independent damage estimate and try to resolve the matter with the carrier. If you continue to have problems, you may wish to contact your state's insurance Commissioner's office and file a complaint.
You also may wish to contact a local attorney and find out if your state has a statute which provides for the award of attorney fees if you successfully sue your insurance carrier for benefits due to you under your contract. If you have such a statute, like the state of Florida has, you should not have a problem in locating an attorney to undertake your representation should the carrier continue to be unreasonable.
Legal Disclaimer:
Mr. Lundeen is licensed to practice law in Florida and Vermont. The response herein is not legal advice and does not create an attorney/client relationship. The response is in the form of legal education and is intended to provide general information about the matter within the question. Oftentimes the question does not include significant and important facts and timelines that, if known, could significantly change the reply and make it unsuitable. Mr. Lundeen strongly advises the questioner to confer with an attorney in your state in order to insure proper advice is received.