Based mainly on Aronson and Kiziria's Georgian Language and Culture: A Continuing Course, the most common situations in which Georgian nouns that take -i in the nominative can end in the bare consonant are the following:
1) vocative forms of proper nouns, e.g. "დავითი/Daviti" (nom.), but "დავით/Davit" (voc.),
2) when as an attribute in agreement with a noun in the dative or adverbial case (i.e. it is declined just like a consonant-stem adjective), e.g. "ბოთლ/botl" (bottle) in "ლინდსი ლოჰანი დღეში ორ ბოთლ არაყს სვამს/Lindsi Lohani dgheshi or botl araqs svams" (Lindsay Lohan drinks two bottles of vodka a day),
3) first names preceding family names, titles etc., e.g. "დავით აღმაშენებელი/Davit Aghmashenebeli" (David the Builder) but "დავითი/Daviti", or "მიხეილ სააკაშვილი/Mikheil Saak'ashvili" but "მიხეილი/Mikheili"
4) the first element of some fixed expressions, mainly involving points of the compass, e.g. "დასავლეთ საქართველო/Dasavlet Sakartvelo" (Western Georgia), but "დასავლეთი/dasavleti" (west).