Galaxie 500 did a few covers, two of which I love. They covered Ceremony and, in my opinion, one of their best songs is their cover of The Modern Lovers Song, Don't Let Our Youth Go To Waste. I really enjoy the Yo La Tengo cover of Here Comes My Baby by Cat Stevens. That band has done an absurd amount of covers. The Postal Service did a classic cover of Suddenly Everything Has Changed. Memoryhouse (a dream pop band) once covered Every Little Thing She Does Is Magic by The Police. I'm a fan of that as well. One of my absolute favorite covers is the Streetlight Manifesto cover of Such Great Heights, the Iron & Wine cover is very good as well. I know you said cover songs, but the Flaming Lips cover of Dark Side of the Moon is great. Also Lykke Li is awesome and you should check out more of her music.
With regards to Ceremony, one of my favourite bands, Chromatics, did a cover of it too, putting a bit of an italo spin to it. Actually, while I'm here, they also covered Kate Bush with Running Up That Hill
Never knew Chromatics did that cover. All that I've listened to by them is Kill for Love, which was a great album. Covering Neil Young is usually a good way to open an album.
It seems that their label, Italians Do It Better, have a thing for covers. I'm just gonna post a bunch now because why not. Dark Day - Hands in the Dark Dark Day - The Chameleon Kraftwerk - Computerliebe Belle Epoque - Miss Broadway And as you mentioned, Neil Young - My My, Hey Hey (Out of the Blue) (interestingly, they titled it Into the Black)