Android: A site called apkgalaxy nabbed my Android app and offers it as an .apk download from their site. What's the best way to get them to take it down?

You need to get a lawyer. With their help you can not only get them to stop, you can punish them in court. What they are doing is clearly copyright infringement. It is not Google's responsibility to help you with this. At best you can make a complaint via DMCA policies to get their website hidden from Google searches, but you can't get the website blocked or taken down by Google. They don't even have that ability.

Todd is correct.  But try to find out what country they are based out of. If its out of a country without strong copyright law you may have trouble suing. And in general if its not in your country of origin you likely have to get representation in that country, which may be difficult or expensive to do. Today, Ip flows freely and quickly across international boundaries.  Unfortunately, our systems of government are still regional and balkanized.

The best this you can do, is to contact them through email. If they don't respond, just add a complaint on http://www.chillingeffects.com and the owner of that website will be notified. Recently a site called http://www.apkforest.com also did the same to my apps. I contacted his email and he removed the content within 10 mins. I was lucky.

I have found many paid apps in that apk galaxy and apk 4 fun, and they are running Google ads.... and Google drive as host ....it is against copyright's ......and another site http://apkart.com file complaint against them or contact them to remove your app..they will remove in within 24 hrs.....