Yeah, that's a tough one. IMHO, AM2/AM2+/AM3/AM3+ still has some life in it... for the appropriate person / user. It wasn't a bad time in computing technology, and it sounds like your rig is DDR3, so it's outdated, a little bit, but not THAT outdated, that it's no longer useful.
I have a couple of AM2+/AM3/AM3+ rigs, that I've offered for the price of shipping to the DC TeAm in our thread for such things. One of the boards has 4x PCI-E x16 (x8/x8/x8/x8) for quad-GPUs, and the other board, has a 990FX chipset, and 2x PCI-E x16 slots, and an x16 (x4 electrical) for a third GPU. Could be nice little mining / DC boxes. Shipping the old heavy cases that they are in currently, is prohibitive, and the cases' conditions aren't great either.
So, yeah, hard to say what to do with them. Too new to be sent to the recycler, they still have some "tech life" left, but too old to be using as a primary rig.
If you had kids or grandparents or something, I'd say, buy a cheap ATX case with a window, and one of those 3x RGB fan kits, preferably the type with the RF remote-control, rather than mobo control, since mobos of that era didn't have the interface header for modern RGB stuff, and build a blinged-out rig for grandparents or kids. They'll never know the difference, technology-wise, as far as the CPU/RAM/mobo goes, as long as it's working properly. (Unless they're a real tech-head, in which case, they're probably reading this right now, LOL.)
Edit: There was someone here, that built / refurbished old PCs, and gave them away at a local Food Pantry. I've thought similar, though I have yet to take action on that idea. I must have nearly 15 "browser-box"-class rigs in my storage, but nearly all with SSDs, so they wouldn't be half bad. (I think that the worst, is either my SFF AM1 quad-cores, or my Ivy/Haswell dual-core Celeron/Pentium rigs. Which isn't really all that bad, for a basic PC for someone that might not be able to afford a "premium" PC. They could have their kids use it for homework..)
Edit: Speaking of which, I'm just going to leave this here, as a sort-of plug. (Mods, forgive me.)
www.internetessentials.com
Comcast/XFinity's low-cost internet program, you have to qualify (Medicaid / Food Stamps recipients are now eligible too!), but if you can get it, you can get Comcast internet for $9.95 / mo all-in, no caps, no taxes, no equipment fees, no credit checks. There are some limitations, besides qualification (can't have subscribed to Comcast in the last 90 days, can't have outstanding debts to Comcast less than a year old, must be in an area served by Comcast, etc), but on the whole, I think it's a good thing.
It's very, very, minimal service, only 15/2 speeds, but it's WAY better than nothing, for families that might have kids that have a REQUIREMENT to do homework online (not unusual these days). Regular $70/mo internet can be too expensive for some folks, even especially seniors living on SS, etc.
(No, I'm not receiving anything for this. Just trying to pass along a Good Deal when I see one. And I'm a happy customer too, using it right now.)
Edit: So yeah, that being said, maybe you could help a senior in your area, sign up for that Comcast program, and then give them the PC, and set it up for them. They might give you cookies!