Memphis, TN obviously springs to mind, as does Alexandria, TN, but there's Cairo, Lebanon, Karnak, Teheran (sic) and Thebes in Illinois, too. And a number of towns in Mississippi, as well, including Egypt, MS. Why are these all so (relatively) near each other. Was there a huge surge in Egyptian/Middle-Eastern interest at the time these towns were founded?
Your hypothesis is basically correct. To say there was a huge surge is probably an overstatement, but there was definitely a noticeable increase of interest in Egypt in the United States in the early-to-mid nineteenth century. Following Napoleon's 1798-1801 invasion of Egypt, Egyptian elements of architecture, furniture, and interior design saw an increase in popularity in Europe. The United States, still taking many of its fashion queues from Europe, picked up the trend, and this was reflected in the built environment
The most well-known result today is probably the Washington Monument, for which the design contest was held in 1825. Egyptian obelisks were popular as monuments and funerary markers. Egyptian architecture was also present, classed as an exotic revival (as was so-called "Oriental Revival" which included Middle Eastern and Moorish influence,) but was never as popular as the more familiar Greek and Gothic Revival, Romanesque, and Italianate Styles. As an example, The Tombs in New York.
As to why the towns are so close together, they are in an area that was undergoing rapid settlement in the 1810s-40s, when Egyptian themes would have been fashionable. There are many American cities out there with those names, like an Alexandria, Indiana in Madison County and one in Campbell County, Kentucky dating from the same period. Naming new towns after old ones was common.
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why did the people of memphis, tennesee decide to name their city after the city of memphis, egypt?