Economics does not need to contain game theory or regressions to be elegant. Take these wonderful examples, in no particular order, most of which are accessible to non-economists.
1. Charles M. Tiebout's "A Pure Theory of Local Expenditures" in The Journal of Political Economy. This paper established the Tiebout model in public economics.
2. Ronald Coase's "The Nature of the Firm," along with his "Problem of Social Cost" made him a big name economist. The first article deals with the organisation of firms, while the second discusses institutional solutions to externalities.
3. Douglass North's articles are generally non-technical. He is better known for his books, but for a good paper, check out his analysis of The Glorious Revolution.
4. "The Use of Knowledge in Society": Friedrich Hayek beautifully defends the market as an optimal way to allocate resources, given our limited individual knowledge.
5. Oliver Williamson resurrected and renewed Coase through his research on transaction costs and economic institutions.
6. Peter Leeson's article on the economics of marine piracy is entertaining, but Leeson dodges the issues of collective action and institutional design. Read it with some caution.
7. Piketty and Saez's presentation of U.S. top income data offers a good introduction to inequality issues.
8. Henrich et al.'s "In Search of Homo Economicus" is a good short article on how different tribal societies play experimental games.
9. Kenneth Arrow's "Uncertainty and the Welfare Economics of Medical Care" shows how non-market social institutions (for example, physician licensing) arise due to market failures.
Those are all the examples I can think of for now. If you have any more, then please let me know!