Agree - it's completely pointless getting free domain or even a cheap one from the bargain basement sites. It will severely disadvantage you for search indexing and ranking. I have had first hand experience of this.
You can get a free one for a year with a hosting plan from GreenGeeks, but then you pay for your monthly hosting, as you should.
You can get reputable domain service from Domain Orb for $9.95 or HostGator for $15 with your hosting account. That's for a year and that's cheap enough.
I don't mean to be rude, but if you're not prepared to pay $9.95 for your domain so it can get ranked on search engines, I have to ask what are you intending to do on the Internet? Be professional if you want to get professional results. It's worth doing thing properly if you're going to put effort into building a website.