Why do they always appear around the mouth?
Simple answer - they don’t.
Herpes Simplexvirus is spread by contact. In humans, a primary contact method is mouth to mouth, thus the connection between HSV and oral infection. Also, the skin round the mouth is well ennervated (HSV infect nerve cells) and fairly sensitive (i.e. able to be penetrated). So HSV generally presents as oral lesions, but not always. Genital herpes are a closely related virus, and oral/genital transmission (of both oral and genital variants) are common (they usually do not become recurrent infections, though). Transmission of viruses to fingers by picking oral lesions is also common.
Other sites are :- hands (particularly round the nail), corneas, gums, oesophagus, neck, shoulders and ears (common in wrestlers, apparently) and brain (which can be fatal or cause devastating brain damage).
So, not just mouths.
So basically the virus does not travel far from the original site of infection?
Correct. It travels up the nerve to the nearest ganglion, then hangs out there for the rest of your life, occasionally going active, forming a sore and shedding baby viruses to go infect your closest friends and family.