What we observe in nature exists in several scales. From the distances of stars and galaxies and clusters of galaxies to the sizes of atoms and elementary particles.
Now we have to define "observe".
Observing in human size scale means what our ears hear, what our eyes see, what our hands feel, our nose smells , our mouth tastes. That was the first classification and the level of "proxy", i.e. intermediate between fact and our understanding and classification, which is biological. (the term proxy is widely used in climate researches)
A second level of observing comes when we use proxies, like meters, thermometers, telescopes and microscopes etc. which register on our biological proxies and we accumulate knowledge. At this level we can overcome the limits of the human scale and find and study the enormous scales of the galaxies and the tiny scales of the bacteria and microbes. A level of microns and millimeters. We observe waves in liquids with such size wavelengths
Visible light is of the order of Angstroms, $10^{-10}$ meters. As science progressed the idea of light being corpuscles ( Newton) became overcome by the observation of interference phenomena which definitely said "waves".
Then came the quantum revolution, the photoelectric effect (Particle), the double slit experiments( wave) that showed light had aspects of a corpuscle and aspects of a wave. We our now in a final level of use of proxy, called mathematics
The wave particle duality was understood in the theory of quantum mechanics. In this theory depending on the observation a particle will either react as a "particle" i.e. have a momentum and location defined , or as a wave, i.e. have a frequency/wavelength and geometry defining its presence BUT, and it is a huge but, this wavelength is not in the matter/energy itself that is defining the particle , but in the probability of finding that particle in a specific (x,y,z,t) location. If there is no experiment looking for the particle at specific locations its form is unknown and bounded by the Heisenberg Uncertainty Principle.
What is described with words in the last paragraph is rigorously set out in mathematical equations and it is not possible to understand really what is going on if one does not acquire the mathematical tools, as a native on a primitive island could not understand airplanes. Mathematics is the ultimate proxy for understanding quantum phenomena.
Now light is special in the sense that collectively it displays the wave properties macroscopically, and the specialness comes from the Maxwell Equations which work as well in both systems, the classical and the quantum mechanical, but this also needs mathematics to be comprehended.
So a visualization is misleading in the sense that the mathematical wave function coming from the quantum mechanical equations is like a "statistical" tool whose square gives us the probability of observing the particle at (x,y,z,t). Suppose that I have a statistical probability function for you, that you may be in New York on 17/10/2012 and probabilities spread all over the east coast of the US. Does that mean that you are nowhere? does that mean that you are everywhere? Equally with the photons and the elementary particles. It is just a mathematical probability coming out of the inherent quantum mechanical nature of the cosmos.
Physics is all about constructing approximate mathematical models to describe the real world. For example Newton's laws are a mathematical model, and they do a pretty good job of describing the motion of the planets round the Sun. Pretty good, but not perfect, because Newton's laws fail to fully describe the motion of Mercury. To fix this we use a more accurate, but also far more complicated, mathematical model called General Relativity. But for most purposes, e.g. sending spaceships to Mars, we don't need the accuracy of General Relativity and Newton's laws will do, which is just as well as GR is extremely hard to do calculations with.
The point of this rambling is that physicists continually face decisions as to what mathematical models to use, and they'll normally choose the simplest one that works. Quantum Electrodynamics is the most accurate theory we have for describing the interactions of light, but it's also very hard and in many cases we don't need to go that far. If you're asked to calculate the diffraction pattern from a Young's slits experiment you can do it to better than experimental accuracy using the wave model: you don't need to use QED.
Feynmann is quite correct that the wave/particle duality is a naive idea, and one now superceded by quantum field theory. But just because an idea is naive doesn't mean it isn't useful. There isn't a best way of calculating the behaviour of physical systems just like there isn't a best car. You could use QED to calculate what happens in the Young's slits experiment, but you wouldn't, any more than you'd use a Ferrari to go to the supermarket.
Best Answer
No, this is not at all how quantum field theory works.
A "quantum field" does not have a definite value at any time, it is an operator in the quantum theory, not something that has a fixed numerical value, therefore representing it as a lattice as you have done does not reflect the quantum nature of the field. This is the classical picture of the field, just like a point particle is the classical picture of the electron, not its quantum picture.
The quantum field and the particle states are different things - the field is an operator and the particle is a state in the quantum theory. You can use (parts of) the quantum field operator to create particles, but the notion of particle is much more elusive than it being a simple ripple in a classical field. For more on this see this answer of mine on real particles and this question and its answers on virtual particles.
The "wave-particle duality" is, in any case, a somewhat vague notion that has no real formal counterpart in modern quantum mechanics. Quantum objects are just that, quantum objects. They have aspects of waves (e.g. they can "interfere", they can obey wave-like equations, they "spread") and they have aspects of particles (e.g. they can (but not must be) localized at "points", they have mass) but they are neither. And I'm sure you can find quantum behaviour that you'll not be able to attribute to either a wavy or a particle nature, such as Bell experiments about entanglement (which cannot be explained classically, and hence any attempt to explain them with a particle or wave picture must necessarily fail).