As China's urbanization enters a stage of high-quality development， urban livability has become a crucial factor influencing the settlement decisions of young migrants. Based on the China Migrants Dynamic Survey （CMDS） data and macro-livability indicators of 261 cities， this study employs a Multi-Level Logistic Regression Model to systematically analyze the heterogeneous impact of urban livability on the settlement intentions of young migrants across different family life cycle stages. The findings reveal that the evolution of the family life cycle profoundly shapes young migrants' settlement decisions， exhibiting a distinct logic of hierarchical transition. Specifically， it shifts from a "survival logic" during singlehood， which highly prioritizes living costs and environmental quality， to a "nesting logic" in the family formation stage， which focuses on housing property rights and asset accumulation， and ultimately evolves into a "parenting logic" in the family expansion stage， which relies heavily on high-quality public services and transport accessibility. Furthermore， city size plays a significant moderating role. Although medium-sized cities offer lower living pressure， they suffer from a shortage of basic educational resources， making them susceptible to the "public service trap". Conversely， large cities exhibit a significant trend of diminishing marginal utility in public resource allocation， where enhancing spatiotemporal service efficiency is key to overcoming the constraints of congestion costs. Therefore， the construction of youth development-oriented cities should avoid homogenized strategies. By establishing a tiered housing support system， implementing differentiated public service reinforcement strategies， and creating a comprehensive livable ecosystem， cities can achieve a win-win outcome for both the permanent settlement of young populations and sustainable urban development.