Originally Posted by monahos
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.
I arrived at INC recently around 2:30 am from Doha, was picked up by Korean collegues/friends and knew there was a meeting in Gangnam 2pm in the afternoon. We headed to a 24h diner in a nearby part of Incheon for some spicy bbq chicken and soup and washed that down with beer and soju. That and the usual Korean Karaoke Bars and Love Motels are all the areas closest to the airport have to offer. Then took a motel at around 5 am, slept til 10 and arrived at the meeting with some jet-lag but in good spirits.
If you can arrange a Korean-speaker as guide, why not go for the real Korean experience, though?