Flarum looks quite nice.
Another thing to consider: do you really need to integrate them? Do regular users need to login on the WordPress side of things, or is it just you and other admins to update site content? Do you need to share data between WordPress and the forum software for some reason?
For example, it's common for WordPress-powered membership sites to restrict content to users with certain capabilities, and restrict bbPress forum access based on the same capabilities. In this case, you'd be better off using bbPress and not worrying about potentially complicated integrations with other forum software.
If you're just concerned with making things look "seamless" between the main site and the forum, there are ways of theming it to look the same without any sort of integration at all.
Basically, unless you have a purposeful reason for doing so, I wouldn't rule out standalone forum software just because it doesn't have a publicly released WordPress integration.
But if you just want a plug-and-play WordPress-powered solution, there's no better option than bbPress. It just works.
By the way, there are a few Discourse <-> WordPress integrations out there already, like this one. It doesn't seem to cover templating, but covers SSO.