They have gotten to the point where they are alright with meeting this person in real life at a public place, but they aren’t sure that this is a person that they want to have their phone number.
By meeting without giving a phone number, they are acknowledging that there is interest, but there is yet to be trust established.
When a person agrees to meet on a date in real life without giving a phone number beforehand, they are indicating that they aren’t ready to take their interaction to the level of exchanging phone numbers quite yet.
Becoming disappointed over how people look in real life versus their online dating profile is something that is a common occurrence in online dating.
You may have had a totally different impression of what this person would look like in real life.
You may have gotten a really good impression through the person’s online dating profile that this person was going to look in a particular way that appealed to you.