No Woman No Cry by Bob Marley
The chords are just C G Am F for the most part, if you play bass you’ll understand the bass riff (the g-a-b-g) going into the C chord.
Then you can combine the chords and melody to do a pretty basic but impressive arrangement
Another would be Still the Same by Bob Seger
Bass/chords on left hand and just triads with the right hand to form the melody, it’s more of a rhythmic thing being rock anyway
PS: learning to play scales and arpeggios like everyone suggests isn’t theory, it’s technique you could train a monkey to do. The most technically advanced pianists I know know NOTHING about theory while claiming to be experts. They don’t even know what chords are in what major key.
You learn theory by doing. Sit down, learn to play songs that sound cool to you, and you learn the theory of the style you like through learning them. If you like rock and roll like I do, you learn a hell of a lot more from just learning a Meat Loaf song and going “ohhhh, I can do THAT chord to give it that sound” or “whoa so that’s how they make that sound the way it does, with that weird note” and you learn 1000x faster and better than people who can play their scales up and down and nothing else
EDIT 2:
I saw you saying something about a party trick. I wanted to learn that too when I was a novice pianist. Great songs for that that sound good…
Bohemian Rhapsody. It’s easy as hell. The crossover with the hands impresses everyone. One of the first songs I learned in 2013 when I wanted to learn it seriously
Somebody to Love too, although that one’s a little more complex.
Also, you don’t have to play perfectly to make it sound good, case in point:
This song is one I learned how to play (more or less, I eared it out) It was in a movie called Palo Alto, and a drunk teenager was playing it at a party and I thought it seemed rock and roll as hell in attitude. Anyway, whether or not you like the music, it certainly has a sloppy drunk ballsy feel to it, and it can be applied to other songs to make them sound more impressive