Ketzos Hashulchan (39:3), quoting the Elyah Rabbah (OC 170:23), who in turn quotes the Rokeach (329), writes that it is common decency to only eat and drink while seated. This is also brought by Ba'er Heiteiv (OC 170:16) and Kitzur Shulchan Aruch (42:2).
The Mishnah Berurah (296:6) writes that one should drink the cup of Havdalah sitting, "because lechatechila one1 should not drink while standing". In contrast, Shulchan Aruch Harav (OC 296:15) writes that after finishing Havdalah one should sit down to drink the cup, "because a Talmid Chacham (Torah scholar) should not eat or drink standing". This is based on the Derech Eretz Zuta (5:1), which specifically states "Talmid Chacham".
As a (slightly related) aside, Shulchan Aruch Harav (OC 199:1)2 writes that a waiter commonly eats standing (and that he can join a zimmun as such), yet the gemara (berachos 52b) states that Beis Hillel holds the waiter must be a Talmid Chacham (and also according to Beis Shammai there is no objection to the waiter being a Talmid Chacham), yet this (that a Talmid Chacham should not eat or drink standing) is not brought as an objection.
1 I.e. everyone, not only Torah Scholars.
2 Quoting Rabbenu Yonah, Rosh, et al.