According to Wikipedia, the Eurovision finals are "traditionally held on a spring Saturday evening." It more often than not is held during the month of May.
Read more about the Eurovision via the Related Link.
The 1978 Eurovision Song Contest was held in Paris, France.
The Eurovision Song Contest 2009 was held in Moscow, Russia.
Finland
Netherlands
Belgrade, Serbia
Russia
France
No, Ethiopia have never entered the Eurovision Song Contest and they have never held the competition either.
The 2012 Eurovision Song Contest was held in Baku, Azerbaijan.
Ireland
The Eurovision Song Contest is held in May at 21:00 CET.
The Eurovision Song Contest 2013 was held in Malmö, Sweden. The winner of the 2013 contest was Denmark, represented by Emmelie de Forestand the song "Only Teardrops". As Denmark won the competition, the Eurovision Song Contest 2014 will be held in the Danish capital of Copenhagen.