Your only options in a 15 minute radius are the airside hotel, and the substantially more upscale (and expensive) airport Hyatt. Neither of which have a neighborhood you can stroll in.

The nearest such hotels would be in Incheon proper, whose infrastructure isn't geared towards foreigners, being a port/not particularly upscale dormitory town for Seoul. There are however a number of inexpensive non-chain hotels there.

If nightlife is a priority, consider a hotel in Kangnam (the southern part of Seoul, home to about half the international hotels), as evening inbound and morning outbound traffic between Kangnam and Incheon is light, making for relatively predictable transit times.