I'll point you again to Pit of Babel who has an interesting post on the famous oil drop experiment which made it possible for scientists to determine the charge of an individual electron, and the fact that electron charges were quantitized, a result that was a key foundation of quantum mechanics.
Take home message: Fundamental discoveries about the microscopic world can be made with cleverly designed macroscopic experiments using equipment you could find in a high school physics lab, good lab technique, and a good theoretical framework that includes equations that address the main sources of messiness that can't be eliminated from the experiment.
Longer term point: Modern physics is real. You can illustrate the core points with relatively straight forward experiments that even an educated layman can understand. Yes, most of the experimental efforts now involve multi-million dollar, if not billion dollar experimental apparatus. But, the far simpler experiments do exist to show that the realm of uncertainty that 21st century experiments are trying to clear up is very small. While no one is arrogant enough to claim that the future of science lies only in the last digits of experimental constants, as they did at the beginning of the 20th century, modern scientists are entirely too humble for their own good about how much they do already know.