For Mythos, there's several dining/nightlife kiosks scattered around (one at IOA and one at City that I know of) where you can make ressies. We ate lunch at Mythos on a Thursday, and we made the ressie at the kiosk the day before.
So I guess I personally know of no number since we've never needed one. Definitely takes a lot of the stress off a trip not having to worry about dining reservations before I even start my vacation
The kiosks are pretty visible. The one in City is off center just a bit in the path headed towards USO & IOA after you're finished with all the moving sidewalks, kind of close to the escalator to get upstairs (the one on the left if you're looking at IOA). I think you can also get party pass nightlife tix for City there, too. They have all the menu items there, as well.
The other one I've seen is at IOA, right around the bridge that the Hulk goes under. I haven't seen one at USO, but I really haven't really looked for it, either (we always eat at Finnegan's and have never needed a ressie).
I understand for Mythos, you can just walk right up and make a ressie for a future date/time.
As far as I know, HRC and Bubba Gump's doesn't accept ressies at all.
Not sure if it's still a perc but, last trip in '05, I called the HRH concierge desk & they set up all our dining res., including mythos, finnegans & Mararitaville. I had to call the Nascar place myself.