“Who are the best SFF publishers who accept unsolicited submissions for novel manuscripts?”
There are many publishers who accept unsolicited manuscripts, but none of them are the big three (or divisions of said companies).
If you are looking to publish your novel with a large publisher you’ll need to be represented by an agent. That will mean finding one who will accept your work and agree to represent you. The hold out on that is huge, for the competition for the good agents is massive. And as a first-time novelist, you will have a lot of hurdles to overcome.
A quick search will show you a number of companies who accept unsolicited submissions. Mentioned prior is TOR books, a Canadian company located in BC. Another one is Science Fiction and Fantasy Publications (I’m a little bias on this one for I know how hard they work). SFFP has published a number of fantastic novels and is an imprint of DAOwen Publications. They are very picky in what they publish and you’ll need to make sure your manuscript is polished before submitting.
You could also dive into the big pool of the self-publishing route, but that could also cause you to be lost in the shuffle and discarded like a lot of those novels. Many self-published books are poorly edited and the general public is now noticing the horrendous quality of the work.
Also, if you do find a publisher who will accept your manuscript, find out about their publishing procedure. One company I know does not edit the submissions, just publishes them as submitted, while another one just does a rudimentary edit to remove glaring errors, leaving a multitude of issues with the stories. Avoid those companies. Make sure the company as at least two editors who will go through your work with rewrite requests. If not, you’ll get delegated to the hack pile for any major publisher. Also find out how they pay royalties. Some only pay annually, while others quarterly (probably the best). You want to get a percentage of the profit generated by the manuscript, not a set dollar value per sale. The reason for that is if the book goes to screen options and you have a per book deal, you could be getting only 10-20 books worth of royalties instead of a percentage of the manuscript sale (the difference is $30-$40 as opposed to $10,000).
Since this answer is now getting involved, I will end it here with the following advice – do your research and good luck with finding a publisher.