The Top 20 Publishers for New Authors at Authors Publish is a list of publishers that authors are supposed to be able to submit to directly. Many of these I haven't heard of, so I can't comment on the quality of the list overall.
However, I have heard of Chronicle Books and Alloy Entertainment, which I understand to be a book packager rather than a traditional publisher. Bloomsbury Spark is connected to Bloomsbury, which is certainly well known. DAW is an imprint of Penguin Books, and Penguin Books is huge.
When you're ready to start submitting, checking these publishers out could be worth your time, especially if you don't have an agent.