Translation:This gallery is not in Kyiv, but in Odesa.
I suppose that is possible, in the context of a pictorial representation of some sort or maybe a written reference. My question, though, is really whether Ukrainians simply avoid "that" and use "this" almost exclusively, as the sentences here do? Does this represent a peculiarity of the way Ukrainians speak or does the Duolingo Ukrainian group just want to use це more for pedagogical purposes--to get the students used to seeing the letter ц or something?
No, we use both, really. Ця галерея, та галерея. Depends on the context in exactly the same way as in English. I, for example, would say "ця галерея/this gallery" when speaking Ukr/Eng meaning this one that I'm talking about now or showing on a booklet or on the Internet; and "та галерея/that gallery" when talking about a gallery I've mentioned before or located far away or contrasting with some other gallery that I called "this gallery"... Really the same :)