Wireless Router To Hub/Switch

I have plugged a router into a router with neither in bridge mode. The DHCP server in the router connected to the cable modem was assigning IP addresses in the 192.168.1.0 block. The second router's WAN port was connected to one of the LAN ports on the first router. The DHCP server in the second router was set to assign IP addresses in the 192.168.2.0 block. I didn't specifically change this (those where the default settings for the two routers). I did this because I needed to set up the second router for use at another location and wanted to make sure everything was working correctly.

Based on your description I am assuming that the building you are moving into has a NAT/router connected to the Internet and is assigning IP addresses. By using your router in the same configuration as when it was connected to a cable modem you still get the LAN isolation and whatever firewall protection the NAT/router provides. I am not sure that all protocols would work in this configuration but you might as well experiment and see if everything you need works.