Yes, closing Guantanamo Bay would have an impact. If only symbolically, it would close a negative chapter in this country's history. It would signify the end of torture and unjust incarceration. No longer would the US be able to use it as a dumping ground to unlawfully hold suspects. It would be a statement of peace and law-abiding well-being for the world.
Guantanamo Bay is a disgrace to everything America stands for. In operating outside the rule of law it fails to provide detainees with the very same civic rights the United States is using as a justification for interventions in the Middle East. If Guantanamo Bay closed the inmates would be transferred to other prisons in the United States, which would make them much more visible and protected for various injustices. Just because these individuals have been deemed terrorists does not mean they do not deserve to be treated as humans and fairly under our legal system.
Just because Gitmo would close, why can't we just throw these terrorists on some island like Guam or some barren place like Alaska? You have to realize that the ones sent to Gitmo aren't there for traffic violations or shoplifting. They are there because they are terrorists. They voluntarily committed acts of aggression against their own people or our troops. You want these monsters to have rights? It's easy to say that when you sit nice and safe in your warm house while across the world American troops are being blown up, shot at, civilians are being blown up by suicide bombers and car bombers and all sorts of other bad stuff. You think the other side is playing by the rules? Our laws of fair justice should be for law abiding citizens of the world. Not some scumbag who shoots an RPG at an American Convoy or sets a bomb up and kills dozens of civilians in a market in the Middle East or the Afghan.
America has so many places that they can take the prisoners away without the American public's knowledge. Nobody would be able to know how any of the prisoners are treated if they make a military post in any other colony that America took control over. Guam, Puerto Rico, and other countries would probably gladly accept a post there.
Closing Guantanamo Bay would make little difference. The detainees would still have to be housed somewhere, and the conditions they would face in any other or regular prison would be the same or worse. The only significance in closing Guantanamo would be for public relations, as it has been painted as being a harsh prison by critics of American policy.