How to redeploy host-manager webapp on Tomcat 7?

You could try reinstalling all of Tomcat or simply download the latest ZIP file from http://tomcat.apache.org/download-70.cgi/ and copy webapps/host-manager to your existing Tomcat webapps dir.

UPD

Ubuntu 10.04 includes Tomcat 6 but I'm guessing Tomcat 7 is implemented in the same way.

The host-manager is installed in /usr/share/tomcat6-admin/host-manager which is referenced by /etc/tomcat6/Catalina/localhost/host-manager.xml. In there, I find:

<Context path="/host-manager"
    docBase="/usr/share/tomcat6-admin/host-manager"
    antiResourceLocking="false" privileged="true" />

sudo apt-get install tomcat7-docs tomcat7-admin

Will install the manager app, which is missing if you only did

sudo apt-get install tomcat7