I recently downloaded most of their albums, and they definitely took a downturn in quality after The Game. I think part of it was them trying to keep up with the trends in popular music at the time, especially synthesizers and the more "electronic" sounds.
Not to mention that the videos for "Body Language" and "I Want to Break Free" were not well received in the US. The former was really racy & sensual, & the latter showed the band members in drag. I suppose it was an attempt to stay with the times, as you said, and make lots of music videos that could be on MTV. But it didn't work.
For Queen songs that I listen to a lot, I'd say anything off of their first Greatest Hits album, as well as deeper album tracks like "Liar," "Ogre Battle," "In the Lap of the Gods revisited," "39," and "Let Me Entertain You."