[chunksmediocrites]

Originally Posted by California Tanker

Aren't there only something like a dozen which the US actually wants to keep,

Miami Herald, June 2013:

In January 2010, the task force revealed that it classified 48 Guantánamo captives as dangerous but ineligible for trial because of a lack of evidence, or because the evidence was too tainted.
...>snip<...
According to the list, the men designated for indefinite detention are 26 Yemenis, 12 Afghans, 3 Saudis, 2 Kuwaitis, 2 Libyans, a Kenyan, a Moroccan and a Somali.

Originally Posted by California Tanker

the other 100 have the minor problem that no other country wants to take them?

The largest contingent by far is Yemeni, followed by Afghans, then Saudis. Then you get down to five Algerians, five Tunisians and five Pakistanis, and then fewer than that for a number of other countries. So let's see if your question can be answered for the majority of prisoners.
Reuters, Aug 2013:

[President of Yemen] Hadi met Obama in the Oval Office a day after he tried to persuade U.S. senators to send home dozens of Yemeni detainees held at the controversial U.S. facility in Cuba.
...>snip<...
Yemen's support is critical to closing Guantanamo because 56 of the 86 detainees who have been cleared for transfer or release are from the impoverished country on the Arabian Peninsula.

The US refuses to release the cleared for release prisoners because Yemen is, according to the US, unstable and a hotbed of radicalism.
Yemen, where the 79 US drone strikes and 58 non-combatant deaths since 2012 have been making Yemen... more stable?
Only a 22% civilian kill rate on those stabilizing drone strikes for 2002-2014 in Yemen. Depending of course, on how you define "combatant":
ProPublica, June 2012:

In a lengthy front-page story last week exploring President Obama's use of drone strikes in countries including Pakistan and Yemen, the New York Times reported that the president had "embraced a disputed method for counting civilian casualties that did little to box him in."

Citing "several administration officials," the Times reported that this method "in effect counts all military-age males in a strike zone as combatants ... unless there is explicit intelligence posthumously proving them innocent."

Afghan prisoners:
Washington Post, Nov 2013:

[President of Afghanistan] Karzai told Rice that he would sign only after the United States helps his government begin peace talks with the Taliban and agrees to release all 17 Afghan citizens being held in the Guantanamo Bay detention center in Cuba, according to Afghan and U.S. officials.

Saudi prisoners:
Guardian, Dec 2013:

Two Guantanamo Bay prisoners have been transferred to Saudi Arabia as part of a renewed effort to close the detention camp.

Algeria?
Guardian, Aug 2013:

The US Department of Defense announced on Thursday it has released two men from Guantánamo Bay prison to their home nation of Algeria.

A Pentagon statement said that the men, Nabil Said Hadjarab and Mutia Sadiq Ahmad Sayyab, had been approved for transfer after a review directed by President Obama. It said it was grateful to the Algerian government for accepting the men.

Tunisia?
Huffington Post, Sept 2011:

Tunisia will soon send a mission to the United States to plead for the repatriation of its five remaining citizens held at the Guantanamo Bay detention center, a Justice Ministry representative said Wednesday.

Pakistan?
There were 60 Pakistani prisoners at Guantanamo; 55 have been repatriated to Pakistan. Looks like Pakistan will take their citizens.

The US prevents the release of prisoners from Guantanamo; the majority of the prisoners are from countries that want their citizens returned.