Custom wp_query – I’m getting ‘all’ post, not the specific post in the query

You should use tax_query for that. See official documentation here.

Try this:

$indicaArgs = array( 
        'post_type' => 'product',
        'productType' => 'Indica', 
        'locationCity' => 'Los Angeles',
        'posts_per_page' => -1, 
        'post_status' => 'publish',
        'tax_query' => array(
          'relation' => 'AND',
            array(
              'taxonomy' => 'productType',
              'field' => 'slug',
              'terms' => 'indica', // here should be slug
              ),
            array(
              'taxonomy' => 'locationCity',
              'field' => 'slug',
              'terms' => 'los-angeles', // here should be slug
              ),
          ),
        'date_query' => array(
                            array(
                                'year'  => $today["year"],
                                'month' => $today["mon"],
                                'day'   => $today["mday"],
                            ),  
                        )
);