If you have installed a single WebSphere Service Registry and Repository (WSRR) then it runs the web interface on port 9443 or 9080 for unsecured. However if you have installed many copies, it is often not obvious which port the web interface is running on.
Luckily there is an easy way to find out, if you have access to the file system. Tucked away in the WebSphere Application Server (WAS) profile is the logs directory, in which there is the file "AboutThisProfile.txt". The path of this file is generally:
WAS install dir/profiles/WSRR profile/logs/AboutThisProfile.txt
Open up that file and it conveniently lists where the web interface is:
Administrative console port: 9073
Administrative console secure port: 9055
HTTP transport port: 9093
HTTPS transport port: 9456
So to log into WSRR, you would use https://host:9456/ServiceRegistry https://host:9456/BusinessSpace or http://host:9093/ServiceRegistry http://host:9093/BusinessSpace. To log into the WAS admin console it's http://host:9073/admin or https://host:9055/admin.
Now where did I put that WAS admin console...