For routine laboratory practice, surface-enhanced Raman scattering (SERS) spectroscopy must be simple, inexpensive, stable for a long time, and reproducible. In this study, we mixed 1 μL of PEGylated silver-coated gold nanorods (Au–Ag NRs) with 1 μL of Raman reporters to obtain, after deposition on a silicon wafer and drying at room temperature for 5 min, a self-assembled NR monolayer with incorporated Raman molecules. In addition, PEGylated NR powders were fabricated and used for SERS in two options. In one, they were used to prepare SERS colloids with a desired NR concentration in a matter of seconds; in the other, they were directly dissolved in a drop of analyte and were then deposited on a silicon wafer. We investigated the SERS spectra of rhodamine 6G (R6G) and the analytical enhancement factor (AEF) as a function of silver shell thickness and NR concentration at 633 nm laser excitation. A very thin (2 nm) silver coating of Au NRs was sufficient to increase the AEF from 103 for Au NRs to 2.5 × 104 for composite Au–Ag NRs. The increase in the NR concentration from 2 to 14 g/L of Au gave a 3-fold increase in the SERS intensity but did not affect the AEF. Three-dimensional finite-difference time-domain simulations confirmed that the electromagnetic mechanism of AEF enhancement for silver-coated NRs was due to the generation of hotspots near the end-to-end and end-to-side nanoparticle contacts. The estimated cost of all reagents for one SERS measurement is about one cent. Coupled with its simplicity, reproducibility, and low cost, the proposed SERS technique can be recommended for routine chemical or biomedical sensing of small analyte amounts with various substrates, such as glass, polymer films, or even Whatman paper.