You can get some domain names for as little as $1/year for niche TLDs, and if you're willing to splurge a bit, you can get more generic ones for $8. It not only looks more professional, it simplifies administration, and makes it far easier to isolate the domains later. You can also extend the branding to email addresses. If they're just pet projects, it's no big deal, but if you're intending to monetize them or want them to become durable brands, the sooner you get them a custom domain, the better.
Private domain is fine if it's just your thing you build at some point. Something I sometimes see people do if things are vaguely related is to get one domain for all of them, with the idea that's it might be easier to remember than your personal domain and makes accessing them faster.
How much control do you have over your existing domain?
You could host them on subdomains:
I.e.: instead of site.com/tool-a
You'd have: tool-a.site.com
And: tool-b.site.com
etc.
The way I see it, hosting them on your personal website portrays them like a portfolio. If they have potential to grow into something on their own you may want to consider giving them their own website to keep it modular. I agree with you, if you're not going to make money off of them, or they won't grow into an open source sensation (even a minor one), why not just keep it on your personal website?