The 15-minute city framework was developed for walking-centric cities and performs poorly in dense South Asian contexts where informal transport—auto-rickshaws and similar intermediate public transport (IPT) modes—is structurally integral to daily mobility. This paper extends the framework to Varanasi, India (1.2 million residents, 90 administrative wards) by quantifying ward-level accessibility to four public service facility categories across five transport scenarios using a two-step floating catchment area (2SFCA) method applied to road network and GTFS data. Ward rankings are derived via TOPSIS, weighted by environmental cost and local travel behaviour; the Next Proximity Index (NEXI) provides an independent proximity benchmark. Walking NEXI scores range from 27.4 to 59.2 across wards; car NEXI from 83.8 to 100. TOPSIS and NEXI rankings diverge systematically, confirming that geographic proximity and multimodal service reach are distinct accessibility dimensions with different policy implications. The 2SFCA-TOPSIS-NEXI framework is replicable across other South Asian cities using open data.