Does Albert Einstein have any living relatives alive today?

Yes, there is a grand daughter still alive. Evelyn is her name.

https://en.wikipedia.org/wiki/Hans_Albert_Einstein

Here are a few more:

His granddaughter Evelyn Einstein, and great-grandson Paul Einstein, descendants of Hans Albert, have sued Paul's brother, Thomas Einstein, and Michael Ferguson...

http://www.nytimes.com/1996/11/06/arts/dark-side-of-einstein-emerges-in-his-letters.html

ALSO: Yes, there are still descendants. They are grandchildren and great grandchildren. However, due to reasons of personality protection their addresses are not published.

http://www.einstein-website.de/z_information/faq-e.html