If I were professionally producing the iHeart Radio Queenbert performance to match the occasion:
The Show Must Go On (to stun them all from the beginning)
Under Pressure (with Bowie! Pretty Please!)
Somebody To Love (the one song Adam makes his own theatrically-speaking)
Who Wants To Live Forever (because it is the best fit for Adam's voice)
Bohemian Rhapsody (because that's the only Queen song Americans seem to know )We Will Rock You (for the musically challenged to clap and stomp to)
We Are The Champions (just because everybody expects it to follow)
If I was planning a concert just for myself, totally ignoring the iHeart Radio occasion and potential audience:
Seven Seas or Rhye/Keep Yourself Alive medley (no WWRY! I have even removed it from my MP3 player list!)
Don't Stop Me Now (one of my favorite Queen songs of all time. Such a feel good song!)
Somebody To Love
Who Wants To Live Forever
Dragon Attack (with lots of dead Elmos)
I Want To Break Free (ripping the pants again would be a nice bonus)
The Show Must Go On
You might notice that I don't have Another One Bites The Dust or Radio GaGa on either list. I personally don't feel Adam's tenor voice fits them as well as some other songs, but I might be in the minority.
In general, picking only 7 songs was the hardest thing I had to do in a long time