Connect to a heroku database with pgadmin

Solution 1:

Open the "Properties" of the Heroku server in pgAdminIII and change the "Maintenance DB" value to be the name of the database you want to connect to.

The default setup is suitable for DBAs et al who can connect to any database on the server, but apparently that isn't true in your case.

Solution 2:

After you change the Maintenance DB name as suggested by araqnid's answer above, you should also add your database to the DB restrictions field because without this you will see thousands of databases and you may not be able to find yours in the list if the list is too long.

More details here - How to hide databases that I am not allowed to access