Well if you knew what port the remote switch was plugged into on the local switch you could do a 'sh port <port #>' in CatOS or a ' sh int fa# status' in IOS and that will show you the MAC address of the remote switch. From there you would have to go into the router and look at the ARP table with a 'sh ip arp' or you might be able to do a 'sh ip arp <MAC address>' and that will display the IP to MAC address mapping for you.
Other than that I don't know of any other way because normal layer 2 switches don't have ARP tables, thus they don't have any IP->MAC address mappings so there is no way to find out a neighbouring switch's IP without looking at a router in charge of the segment.
