Editing the templates or StyleVars is correct.
Unless I'm reading your question wrong, you want the textbox wider? If yes, then you can do so in StyleVars "Message Area Width (pixels)". You can set the width in pixels.
Or...
You can set the width and height manually by going into template "editor_toolbar_on" in Editor Templates and find lines (near bottom):
Code:
<textarea name="message" id="{$editorid}_textarea" rows="10" cols="60" style="display:block; width:$stylevar[messagewidth]; height:{$editor_height}px" tabindex="1" dir="$stylevar[textdirection]">$newpost[message]</textarea>