Because of their small size, low loss, and compatibility with magnetic fields and elevated temperatures, surface acoustic wave resonators hold significant potential as future quantum interconnects. Here, we design, fabricate, and characterize GHz-frequency surface acoustic wave resonators with the potential for strong capacitive coupling to nanoscale solid-state quantum systems, including semiconductor quantum dots. Strong capacitive coupling to such systems requires a large characteristic impedance, and the resonators we fabricate have impedance values above 100 $Ω$. We achieve such high impedance values by tightly confining a Gaussian acoustic mode. At the same time, the resonators also have low loss, with quality factors of several thousand at millikelvin temperatures. These high-impedance resonators are expected to exhibit large vacuum electric-field fluctuations and have the potential for strong coupling to a variety of solid-state quantum systems.