When U.S. combat forces leave Afghanistan by the end of 2014 there will be no more launching of drone attacks on neighbouring countries from Afghanistan claims the Afghan Foreign Minister Zahay Rasool. The CIA launches attacks on the Tribal Regions of Pakistan at present from Afghan bases.
Before relations with Pakistan went downhill after the shooting of Pakistan soldiers by the U.S. in a border incident a base in Pakistan was also used. Now that base is closed. However this just means that drones will need to fly further. There is an important base in Djibouti and other bases are planned on the Arabian peninsula. There is also a base in the Indian Ocean at Diego Garcia.
The U.S. and the Karzai government have been negotiating the terms of a U.S. presence in Afghanistan after combat troops are removed by the end of 2014. Plans are for a U.S. presence to remain for years if not a decade even after security is supposedly turned over to the Afghans. For more see this article.