http://www.terrific-scientific.co.u...tomic_ionic.gif
This schematic resembles, specifically, a Bohr model of the atom, designed for understanding quantum behavior involving electron shells. It is not meant to be a literal depiction of atomic structure.
These days, when physicists do try to visualize what an atom might actually look like, it's more along the lines of a fuzzy, spherical cloud with a teeny, tiny dense dot at its center (the fuzzy cloud representing electron probabilities).
Your thinking--essentially involving scale--is not entirely off the mark. There may well be beings so advanced that Humanity, by comparison, is far beneath their notice (this is one of the answers given for the Fermi Paradox: if aliens are out there, where are they?). But in no way (at least as far as anyone knows) are atoms like miniature solar systems. If nothing else, different physical laws dominate (ie, quantum mechanics vs relativity).