Any Russians in the house??

I'm not Russian or Russian born but I know some people who are. One of my oldest friends - from childhood - had literally no accent at all; no one would have ever guessed that he was Russian born.

A newer friend is Russian born but in the US a long time. His accent is slight - it's more in intonation that accent, the way he may say certain vowels. I don't know quite how to describe it but I will say that in small town middle America, the majority of folks have difficulty figuring out just what his birth nationality is - all they can tell is that he's "foreign".

Do you need her to be recognized as Russian on the basis of her accent?

I'm Slovenian, and like in other Slavic languages, we often spell or pronounce cities and countries names different ways as anyone from the English speaking world. Russia is Rusija, Moscow is Moskva, and so on. So your character might 'accidentally' use the Russian words for Russian proper names.

In Slavic languages, the letter r, no matter in which position in the word, is almost always pronounced as a sharp r (like in bRagging), so your character would very likely pronounce Russian cities this way: PetRogRad, and maybe sometimes American cities, like New YoRk.

As I've noticed (and experienced...) many of us find hard to pronounce words containing "th" properly, so "this" becomes dis, "authentic" becomes autentic and so on. So, this and sharp R gives this "Russian accent" (youtube video).

This is less a matter of pronunciation than of intonation, but my Czech relatives had a tendency to stress the first syllable of words—PRO-nounce rather than pro-NOUNCE.
They would also roll their R's and use European vowels.