This is where my parents used to donate but they have a limited scope and are no longer in my area;
https://www.purpleheartpickup.org/
Luckily they work through a group called GreenDrop who DOES operate in Virginia and serves several really decent charities;
https://www.gogreendrop.com/who-we-serve
I also really like habitat for humanity for furniture/weird stuff. They're still Christian but Christian doesn't inherently mean bad. HfH does some very real good work.
If you can't find these I'd research local groups of course, especially those with truck porch pickups. I will say this; Goodwill sucks but Salvation Army sucks WAAAAAAY more. If you don't have a lot of options, go for the one that does the least harm. Local thrift store>Goodwill>SA. Salvation army is JUST the absolute rock bottom worst of the worst. They are literally a cult. The words I have for my feelings about them aren't permitted on this website.