The rocket itself is magnificent, yes, but with so many ins and outs to it, curious if the entire design was solely purpose built, or if there were features specifically for aesthetic purposes.
I don't know of any features on the Saturn V that are solely aesthetic in purpose. The flags and USA markings come closest, but they are ostensibly there to identify the origin of the vehicle. The overall white paint scheme is to minimize heating of the cryogenic propellant tanks from sunlight. The interrupted black stripes along the fuselage provide visual/photographic reference points, particularly helpful in seeing if the vehicle is changing its roll attitude and determining exact rates of motion in frame-by-frame photo analysis.
The overall long and skinny cylindrical shape, and all of the large-scale features, are functions of aerodynamics and manufacturability as well as the functions of each part. The proportions are not necessarily optimal for either of those major constraints, and some engineer's aesthetic sense (or Wernher von Braun's) may have influenced them, but engineering requirements certainly dominate the silhouette.
The conical fairings at the base of the first stage are needed to streamline the outboard engines, which are mounted at the edge of the stage; their shape was probably chosen for ease of manufacture rather than for aesthetics or optimal aerodynamics.
It's occasionally claimed that the fins on the first stage have no function and are a purely aesthetic choice on von Braun's part. This isn't quite true. The fins are fixed in place; attitude control during the first-stage burn is performed by the gimbaled first-stage engines. The fins do help keep the stage from tumbling during the first-to-second-stage separation, and in some catastrophic multiple-engine-failure situations, would keep the rocket stable long enough for the launch escape system to get the command module away. They probably would have been deleted to save weight if more Saturn Vs had been ordered.
A non-tapering or slowly-tapering shape is good for aerodynamics, especially at transonic and supersonic speeds; some drag is induced at each change in diameter, so you don't want to do it abruptly or without good reason. The five engines of the Saturn V second stage forced its diameter to be similar to that of the first stage, so it was convenient to make it identical.
The third stage, S-IVB, was also used as the second stage for the smaller Saturn I-B launcher, and its diameter matched that of the Saturn I-B first stage, avoiding a taper there.
The tapered adapter section between the third stage and the Apollo CSM is just large enough to contain the LM and the very large engine bell of the CSM; the conical shape of the command module is established by its method of re-entry, and so on.
I'm sure some of the Saturns carried some kind of graffiti or assembly workers' signatures somewhere in the interior of the assembly, which you could call a form of art, but those aren't designed features.