Personally, I am comfortable with doing this in my home. Additionally, my neighborhood/house/yard is a selling point, so it is to my advantage to meet here.
Rover's Meet and Greet information states, quote, "Meet & Greets usually take place at the home where the booking will occur. However, you’re welcome to arrange the first meeting in a public place like a coffee shop or dog park if that makes you more comfortable."
I only do boarding/daycare, and if the potential client is male my I make sure the husband is there. I've never had any men misrepresent themselves as women, I HAVE had women set up accounts in their husband/boyfriend's name, presumably for safety reasons.
The only problems I've had with people are with them not being forthright about their dog's personality/behavior. That is frustrating, but is not remedied by a change in venue.
Being a person that receives most of their business from House Sitting & Dog Walking, I always offer to travel to the owner's home so they can show me around, I get to see the dog in it's normal environment, and basically allow the owner to ask whatever questions in a form of an interview!
I always do them at the park near my house. I bring my dog there as well.
I personally do meet and greets in the person's home that I will be staying at or watching the dog at. I usually will look the address up before confirming to meet there, just so I know it is safe. This seems to be the most comfortable place for the dog to meet as well.
You could, but my benefit is to see how they fit into my environment and get along with my dogs. Dogs don’t act the same in different places so I wouldn’t waste my time somewhere else if they were boarding but if for a walk it might be ok.