Here is an article from Ramtech development expert on how to bypass the port 8080 and make the tomcat application working without it on the main browser. You can follow the simple instructions which is for the tomcat7 and more or less applies to even tomcat6 and enjoy the java application from tomcat with showing the port 8080.
1. Go to conf folder in tomcat installation directory
e.g. C:\Tomcat 6.0\conf\
2. Edit following tag in server.xml file
3. Change the port=8080 value to port=80
4 Save file.
5. Install authbind
sudo apt-get install authbind
6. In etc/default/tomcat7 set AUTHBIND=yes, to avoid a PermissionDenied error for the port 80. –
7. Run the following commands to provide tomcat7 read+execute on port 80.
sudo touch /etc/authbind/byport/80
sudo chmod 500 /etc/authbind/byport/80
sudo chown tomcat7 /etc/authbind/byport/80
8. Restart tomcat:
sudo /etc/init.d/tomcat7 restart