It's so hard boiling the new tracks down to a top 3. I'd go this direction:
Best - Original
Electrodrome - I actually love this course. It is so atmospheric, and I love the little details like the trails the karts leave on certain sections of the track. You can tell they had a lot of fun making this one.
Mount Wario - I love the story this course tells. It's like a celebration of everything we love about mountains. The natural beauty at the summit and in a mountain forest, the clean energy we get from hydroelectric dams, the excitement of an olympic ski event. The reveal of the crowd waiting at the end as you come through the blue starting gates has an incredible sense of scale.
Bowser Castle - This is the most heavy metal thing that's ever appeared in a Mario game. And it knows it, too, because the start of the race starts with a killer guitar wail. Recreates the feeling of dread I had as a child entering bowser's castle in Super Mario World. Love the flight through the plumes of lava near the end.
Best - Retro
Royal Raceway - Beautiful, peaceful, and the best "asphalt racetrack" style course in the game.
Moo Moo Meadows - I'm not even that into the design of the track itself, but the atmosphere and the music is just so quaint and charming. It's a generous, relaxing course.
Rainbow Road - Yeah, it's hard to top what may be the Citizen Kane of Mario Kart tracks (I know, I know).
Worst - Original
Bone-Dry Dunes - I hate to put this here, because I actually like the way it plays, but it's just aesthetically boring. Color palette is all red-brown, all the time. I wish they had explored more of the desert canyon theme, or the boneyard theme, or the marketplace theme that appears just at the end but nowhere else.
Sunshine Airport - Inside the terminal is beautiful, love the architecture of the ceiling, especially. Too bad the course takes place mostly outside on the runway, which is so much blander in both aesthetics and gameplay. Should have made the terminal bigger and the runway section tighter.
Mario Kart Stadium - I love the way this course looks, but was disappointed that it plays pretty much like a Luigi Circuit would in another Mario Kart game. Not bad, but safe.
Worst - Retro
Sherbet Land - I've played a lot of Double Dash. This was always one of the worst courses in that game, and it's still pretty bad here. The underwater sections don't add much for me. Just bring back DK Mountain and Mushroom City, guys. I don't care that it's been done, put DK Mountain and Mushroom City in every Mario Kart. And bring back Block Fort from N64.
Donut Plains 3 - Doesn't do that much for me. I like the way the SNES graphics are portrayed, though, that is genius.
Wario Stadium - My least favorite of the Wario stadium levels. Coliseum from Double Dash would have been better here, imo.