So you bring your site on localhost for some testing or faster developing and then you get not accessable admin section? Somehow drupal has problem with this and "check update module", so what you need to do is disable it.
To disable the Check Update module without, go to your mySQL database page (phpmyadmin) and select system table. Select the record which filename field="modules/update/update.module". Change the value of status field to 0.