Are you trying to find the bootloader section or just looking in general? If the router is a Linux (busybox) distro, the EEPROM is mapped by the Kernel into sections that are described in the Kernel bootlog. You should see the Bootlog over your serial connection when the router is cold starting.
The kernel bootlog might look something like:
00000000:0001ffff u-boot
00020000:0011ffff kernel
00120000:007dffff rootfs
007e0000:007effff config
007f0000:007fffff art
Although everything is compiled binaries, there might be some interesting strings in the rootfs - such as the configuration web pages.
+ You might come across 'UBI volumes', which are used to partition big NAND flash EEPROMs, generally not little 32K chips.