Promoting the coordinated development of basic public services, urbanization, and tourism is crucial to the high-quality development of regional economies. Taking China’s provinces as the research unit, an evaluation system was constructed, and the spatial and temporal evolution and influencing factors of the coordinated development of the three systems from 2010 to 2020 were measured using the coupling coordination model and geographical detector. The results demonstrate that: (1) From 2010 to 2020, there was a rising trend in basic public services, a declining trend and fluctuating stability in urbanization, and an inverted ‘U’ change in tourism; (2) the degree of coupling coordination was in a mild coordination state and showed an upward trend, with spatial distribution being high in the east and low in the west; (3) the degree of coupling coordination was spatially concentrated. The core hot-spot area was mainly in the southeast coastal area, and the core cold-spot area was mainly in the northwest inland area, showing a spatial distribution pattern of hot in the east and cold in the west; (4) the main influencing factors in the spatial difference in coupled coordinated development were per capita GDP, road network density, per capita disposable income of residents, urban unit employees, total import and export of goods, per capita fiscal expenditure, and number of tourists; (5) endogenous power (economic pulling power, infrastructure support power, industrial driving force, population agglomeration power) and exogenous power (government regulation power, market promotion power, social security power) together promote coupling coordinated development.