To be more illustrative, I modify the initial example:
In[1]:= g = {{{{{{{a, b}}}}}}, {{{{a, b}}}}, {{{a, b}}}, {{a, b}}, {a, b}, c};
locVar = {a, b};
Table[Replace[g, locVar -> 10, n], {n, 1, Depth[g]}]
Out[1]= {{{{{{{{a, b}}}}}}, {{{{a, b}}}}, {{{a, b}}}, {{a, b}}, 10, c},
{{{{{{{a, b}}}}}}, {{{{a, b}}}}, {{{a, b}}}, {10}, 10, c},
{{{{{{{a, b}}}}}}, {{{{a, b}}}}, {{10}}, {10}, 10, c},
{{{{{{{a, b}}}}}}, {{{10}}}, {{10}}, {10}, 10, c},
{{{{{{{a, b}}}}}}, {{{10}}}, {{10}}, {10}, 10, c},
{{{{{{10}}}}}, {{{10}}}, {{10}}, {10}, 10, c},
{{{{{{10}}}}}, {{{10}}}, {{10}}, {10}, 10, c},
{{{{{{10}}}}}, {{{10}}}, {{10}}, {10}, 10, c}}