Find a no-kill shelter. They're a MUCH better alternative than your normal run-of-the-mill shelters that destroy healthy dogs just because they're running out of space. Most of them also have fostering.
I also would never EVER advise to advertise a puppy "free to good home" under any circumstances. One - people will assume there's something wrong with it even after telling them the whole story. and two, it makes it very very easy for someone who may come across as a financially stable person with good intentions to come along and deceive the hell out of you for a free puppy. They MAY have good intentions, but a free dog? They'll take it without caring about needing vet costs, training costs, etc.
I would highly advise looking for a no-kill shelter and asking them if they have a fostering program. I know several foster owners of dogs, and a local no-kill shelter has a fostering program that's VERY well structured. A no-kill shelter is honestly probably your best bet right now, and a lot easier on the dog as they will be gentle on transition.
Edit: Might I suggest then, that you do NOT try to find the dog a home in your area then. If they cannot afford to pay for a dog and need to get one for free, they will NOT have the money to care for it properly. It doesn't matter if the breed is "popular" or not. By giving the dog to a poor family, you're setting the poor puppy up to fail. Vets cost thousands of dollars sometimes in ONE vet visit. There's emergencies where the dog will need at least ONCE in its lifetime that costs extra consultation fees alone. This dog needs to have a home that ISN'T so poor that can't afford a dog by any other means but having it given to them. If you need to help the no-kill shelter by finding it a home, look for families who can not only afford thousands of dollars in vet bills at a moment's notice...but would be able to purchase a puppy from a reputable breeder...then you will know the puppy is going to a place where the family can afford to take care of it long term. If a person can't even afford to purchase a puppy or dog in the first place, they can't afford a dog in the long-term. Harsh, but true. But yes, stick to a no-kill shelter. They will screen potential new owners for financial stability as well as putting the dog in the best place he/she can be.
And just for the record, I would much rather pay for a dog, personally...than be given one for free. ;) A lot more of my own personal worries would be soothed (just as long as the person selling isn't trying to make money from it) and also to ease the mind of the seller that I CAN afford to look after the dog. No matter what breed it is, if I fall in love with the dog, I'll pay for what it is worth.
Edited to add as well: I'm seeing a little bit of Jack Russell Terrier in the dog...and that's a fine breed. Maybe a tiny but of Corgi as well, but I can't tell. There's definitely Jack Russell there though.