Where do companions go when dismissed in Fallout: New Vegas?

Boone and I have been murdering our way through the Mojave Wasteland for the last ingame month or so, and we're very happy together. However, I've just reached Trading Post 188 and encountered Veronica, who claims to wish to join my quest. I know that there's a room in the Lucky 38 where companions go if dismissed, but I haven't been to the Strip yet, and I'm worried about what will happen to my murder buddy if I leave him alone in the wastes.

Where do companions go when dismissed in Fallout: New Vegas?

When dismissed, you can choose whether your companions return to your suite at the Lucky 38 or the location you originally met them.. This travel is immediate, they do not walk through the wastes.

(Note: The option to send them to the Lucky 38 only exists if you have unlocked it by speaking to Mr. House.)