Nook Simple Touch IP Address Range
In case anyone has this same issue, it's solved by assigning a static IP address for the Nook's MAC address under the LAN DHCP Server tab - in my case, under 192.168.1.100 (I didn't experiment to determine what the range of IP addresses would or wouldn't work -- maybe just setting any address as long as it's static works):
Our Nook Simple Touch would connect on almost any other Wi-Fi connection and could shop and download books. But on the RT-N66R(U), it would connect, and the router assigned an IP address, but couldn't get through to the Internet. Since the default IP address range is 192.168.1.2 - 254, and the router had assigned 192.168.1.227, I figured I'd bring it down by putting the Nook on 192.168.1.70. So either it's just a lower address that solves the problem or it's the static assignment.