From time to time due to server loads , updates and package downloads become slow or the server can not be reached.  Both the the Update Manager and Package Manager have tools to find the best mirror to connect to.

Update Manager

Open the Update Manager by clicking on the Update Manager shield icon on panel. Click Edit in the menu, then Software Sources,  click the Download from dropdown and click Other, then click Select Best Server button in the upper right corner of the dialog. After the best server has been found, click Choose Server.  Close the dialog box and click Refresh in the menu. Then Install Updates.

Package Manager

Open the Package Manager (Synaptic). Click Settings, in the menu bar, Repositories,  Download from dropdown and click Other, then click Select Best Server button in the upper right corner of the dialog. After the best server has been found, click Choose Server.  Close the dialog box and click Reload in the menu.

MINT 15

In Mint 15 , Package Manager and Update Manager no longer function as above.  To select the fastest mirror, go to Software Sources in the Preferences menu.  Click on Main in Mirroes section, the mirrors will be tested and fasted ones shown.  Select the one that has the best speed.