Translation:These cities are by the Black Sea.
As far as I know, proper nouns are properly (;-)) capitalised in Hungarian as well as in English. Are you confused about words related to country names? It seems to me that in Hungarian only the actual names of the countries (so the 'basic' proper nouns) are capitalised. See: 'lengyel' is only an adjective meaning 'Polish'; 'Lengyelorsag' means 'Poland' and it is capitalised. On the other hand, 'lengyelül' is not. The system varies from language to language in general. :)
No, they shouldn't be capitalised. Actually, it seems it is English that is more unusual in this sense, for capitalising more stuff compared to other languages. I've found a Wikipedia article that casts some light on the issue of capitalisation in Hungarian: https://en.wikipedia.org/wiki/Hungarian_orthography#Capitalization . I just hope it's correct.