Radak #1: This is like Batei ha'Mevashelim. The singular is used for the Klal. This is like "Lo Seshev Ishah Li b'Veis David Melech Yisrael Ki Kadosh Hemah" (Divrei ha'Yamim II, 8:11) is like b'Vatei. They are the places of ha'Mevashelim, i.e. those who cook.

Radak #2: These are the places of cooking, or the pots, like "u'Mevashelos" (23).

Radak citing Targum Yonasan: The place of preparing food.

Radak: They are Kohanim, who cook their portion (Chazah v'Shok) of Shelamim in these places in Ezras Nashim. One may eat Kodshim Kalim in Ezras Nashim and also outside of it, in the entire city, until the walls of Yerushalayim. Also Yisrael may eat their portions in Ezras Nashim if they want.

Rashi: It is Chazah v'Shok of Shelamim. They are not disqualified via leaving Ezras Yisrael like Chatas and Asham are.

Radak: It is Shelamim, which the nation has a share in it. Kohanim receive Chazah v'Shok, and the owner gets the rest of the meat.