First, your English is great, Tanyusha! No worries there. 

Second, as a man, I certainly would not be expecting any sort of gift. Especially if it's a first meeting. If a woman insisted though, I'd personally like something that represented the woman's country. Ukraine in this case. A book, photo, or something that represents Ukraine or your specific city.

There was a woman I visited fairly often outside the USA who once surprised me by buying me a wallet. The currency in her country was wider than US dollars so I had a hard time carrying around money in my US wallet without it falling out. I thought her gift was really thoughtful as well as helpful. I had met her several times before this though.

In all honesty, finding a great woman that is willing to meet in the first place is probably enough of a gift.