City      Country
-----------------
NY            US
LA            US
Paris         France
Roma          Italy

Place        Score         ID_ref
----------------------------------
Paris         +1            0010
US            +5            1000
Italy         -8            3020

Place        Score            ID_ref
------------------------------------
Paris         +1            0010
France        +1            0010
US            +5            1000
LA            +5            1000
NY            +5            1000
Italy         -8            3020
Roma          -8            3020

pd.concat(
   [df_p.set_index(df_p['Country']).rename_axis('Place', axis=0).stack().reset_index().merge(df_2),
    df_p.set_index(df_p['City']).rename_axis('Place', axis=0).stack().reset_index().merge(df_2)],
   ignore_index=True).drop_duplicates()[['Place','Score','ID_ref']]

Place  Score  ID_ref
0     US      5    1000
1     US      5    1000
2     US      5    1000
4  Italy     -8    3020
5  Italy     -8    3020
6  Paris      1      10
7  Paris      1      10