I am often asked this question, especially when it is a girl-child. BCG vaccine is normally given on the upper and outer aspect of the left upper arm, close to the shoulder.
While I appreciate that you are looking at the cosmetic angle, BCG vaccine should not be given at other sites for the following reasons:

1. About 1-2% of all babies who receive BCG develop a swelling in the [simple_tooltip content=’glands’]lymph nodes[/simple_tooltip] that drain the area of injection. In the case of the upper arm, the draining nodes are in the [simple_tooltip content=’armpit’]axilla[/simple_tooltip] and can be easily detected and treated. If suppose BCG is given in the upper thigh, the draining nodes are in the [simple_tooltip content=’groin’]inguinal region[/simple_tooltip]. It is difficult to pick up these nodes and far more difficult to remove surgically, if required to.
2. As doctors, we are used to looking for the BCG immunization status by looking for the scar in the upper arm and if not present at its usual site, may result in unnecessary administration of BCG twice.