Instagram usernames can only be up to 30 characters in length, and to be valid must be made up of any of only letters, numbers or underscores. (source)

This page lists random Instagram username suggestions, all of which are 30 characters long or less.

More options?

If you want to use your own word in your username, you can use this username page, enter your own word and set the "length limit" field to 30, and then click on "get usernames".