We use SCUBA 850 µm and CO observations to analyze the surroundings of three Galactic ring-like H II regions, KR 7,, with the aim of finding sites of triggered star formation. We find one prominent submillimeter (submm) source for each region, located at the interface between the H II region and its neutral surroundings. Using Two Micron All Sky Survey photometry, we find that the prominent submm source for KR 120 probably contains an embedded cluster of young stellar objects (YSOs), making it a likely site for triggered star formation. The KR 7 sub-mm source could possibly contain embedded YSOs, while the KR 81 sub-mm source likely does not. The mass column densities for these dominant sub-mm sources fall in the ∼ 0.1 − 0.6 g cm −2 range. The mass of the cold, dense material (clumps) seen as the three dominant sub-mm sources fall around ∼ 100 M ⊙ . We use the SCUBA Legacy catalog to characterize the populations of sub-mm sources around the H II regions, and compare them to the sources found around a previously studied similar ring-like H II region (KR 140) and near a massive star-forming region (W3). Finally, we estimate the IR luminosities of the prominent newly detected sub-mm sources and find that they are correlated with the clump mass, consistent with a previously known luminosity-mass relationship which this study shows to be valid over four orders of magnitude in mass.