More commonly, you have x-ray diffraction crystallography. If materials were not composed of atoms, then x-rays would pass through the homogeneous material and leave an even pattern. They do not, they diffract (are deflected) off the atoms in a material. This not only shows the material is made of atoms, but you can also calculate the atomic locations from the diffraction pattern. This is used on a regular basis (as in many times every single day) to figure out the structure of proteins and other complicated molecules. An early application was to find the double-helix structure of DNA.
Second, it's not and never has been, a requisite to be able to observe something directly to 'know' that it exists. If you see dog poop and hear barking there's probably a dog around, even if you haven't seen it.
To begin with, all of chemistry is based on the theory that stuff is made out of molecules, which are formed from atoms, belonging to various elements. That's was pretty much universally accepted by chemists since the Karlsruhe Congress of 1860. There was simply no other way of making sense of chemistry that worked. And that was long before anyone had any idea of what 'atoms' might be made of.
Physicists had universally accepted the idea of atoms as a physical reality (rather than some "chemical" theory) by 1911, with the publication of Jean Perrin's http://www.archive.org/details/atomsjean00perrrich" [Broken]. If your friend is skeptical, let him read the book that settled the debate.
Or, give your friend a good book on the history of science, or, you could point to the excellent three-part BBC documentary "Atom".
The topic of the existence of atoms hasn't been up for any real debate for a century. You might as well claim the world is flat and that satellite photos are fake.
I think he's not challenging the fact whether atoms exist or not, but rather questioning the possibility of really "seeing" them.
Of course, the photos are not fake - what your friend probably saw are the STM images, which I believe, is currently the best way to convince yourself atoms exist if you are really convinced by 'seeing'.
But of course, seeing dog poop and hearing barking are really NOT the same as seeing the dog itself, so I think in that sense, NO, we haven't seen the atoms yet.
I am not so sure whether HUP poses a limit on whether atoms can be MORE directly probed or not, but STM images come really close.
What we are really seeing in an STM image is just the local density of states, not really the nucleus itself.
Maybe before we actually see the electron, one day we'll really be able to see the nucleus of a single atom.
Actually, it's impossible to "see" atoms (much less nuclei) in the conventional sense, because light will not reflect from anything significantly smaller than its wavelength - like an atom, for instance. Atoms are much smaller than the wavelength of visible light. Basically this is saying that it's physically impossible to build an optical microscope powerful enough to see an atom.
However, you can use electrons (or X-rays, but that's more difficult) in place of visible light. The electrons used have a much smaller wavelength than visible light, much smaller than the atom in fact. The process of reflection works pretty much the same way as with visible light, so pictures of atoms obtained by electron diffraction are just as valid as pictures of bacteria obtained with a regular microscope.
At even smaller scales, by using increasingly more energetic electrons with shorter and shorter wavelengths, you can make more and more detailed pictures of atoms and even subatomic particles. But there are a couple of problems to deal with: first of all, the more energy you want to pack into the electrons, the bigger the device you need to do it. That's why physicists build particle accelerators like the LHC: all the accelerator does is put enough energy in the electrons to let them see the detail of what protons and neutrons are made of. The other problem is that sometimes when you try to bounce an electron off, say, a proton, there's so much energy that it winds up breaking up the proton entirely and producing a whole bunch of particles that weren't there before. Of course, there's a lot you can learn by observing which particles are produced, how fast they're moving, which direction they fly out, etc., but that's way more complicated than just taking a picture.