If your garbage gets picked up on Yom Tov are you allowed to bring back into your property your garbage pails on Yom Tov?
AFAIK, at least in general, something considered muktze at the start of yom tov is muktze for the entirety of yom tov ; something like garbage for which there is no use (or which is maus or which is specifically set aside for non-use) is AFAIK generally muktze ; and a basis (base, or container, or support) for only muktze things is generally AFAIK muktze . Putting those three things together would seem to imply that a garbage can cannot be brought back in on yom tov. But, as always, CYLOR!
 E.g., Sh'miras Shabas K'hilchasah (Hebrew edition) 21:1, 20:3, 20:46, 22:1, 22:8.
 E.g., SSK 20:25-27, q.v. and cf. 20:41 paragraph 3.
 E.g., SSK 20:46.
You are allowed to bring them back in. See Rivevos Ephraim 1:222:19 who writes that you can do so as you'll need to use it for more trash, and you may be worried that someone will take your trash can. It would be ideal to wait until after Yom Tov, though.
A garbage pail that contained garbage at the onset of Y"T is muktza because it is "basis" to a muktze.
If emptied on Y"T by city sanitation, you are not permitted to return it to its place. This is because it was muktza at nightfall (bein hashmoshos), and that renders it muktza for the remainder of the day (known as "migu dIskatzoi").
However, on the second day of Y"T, it is permitted. The rule is that which is muktza due to its state during the previous nightfall does not renew during a subsequent nightfall.
As always, consult your rabbi. It is possible that your rabbi would consider a (dirty) garbage pail intrinsically muktza.