I prefer an actual menu. Not one of the deeply nesting, expands on rollover sorts of menus (about half of them disappear if you mis-mouse out), but just a handful of clickable text buttons or whatever that hit the major navigation points.
BigCorps Inc. don't like these, because each menu choice has 3 departments and 14 sub-departments that mate-guard their particular menu area, so designers just give up on mobile and hide it all behind the hamburger icon.
It's absolutely daft. Your Web site should be an extra employee, never-tiring, always at work, facilitating the customer or visitor's needs. It's really weird, but depressingly predictable.
I don't think the org that I work for has really found it.
Enlarging the menu so its easier to find with screen reader tools like TalkBack and VoiceOver has been somewhat effective. However, if you have split menu's, login, search and other features, you start running into complex design issues with where to put all of those and whether you want to stuff them all in the mobile menu, outside the menu or a combination of the two. When you start putting features like search and login into the mobile menu, that also creates more accessibility issues as well.
Designing for accessibility can get really complex, really fast and I'm not sure there's really a solid design pattern yet that addresses all of the issues we're seeing now.
I know that's not a great answer, but it just highlights the complexity of designing for accessibility.
