What is the subcellular location of synthesis of non-essential amino-acids?
There are several enzymes involved in amino acid biosynthesis. These some of thse enzymes are encoded in the human genome. You can check out KEGG for a detailed pathway in different organisms. 



The green arrows denote reactions (and enzymes) that are present in a given organism (Homo sapiens, in this case). If you click on the arrows you can know the details about the enzyme. 

These enzymes are present in the cytoplasm as well as in mitochondria. Moreover, the reactants for synthesis of certain amino acids are produced in mitochondria (TCA cycle intermediates). See this article on the role of mitochondria in amino acid metabolism.


  
  Overview of the amino acid metabolic network in human mitochondria. Shaded areas represent the cytoplasmic segments of the pathways.