AgoraDesk [1] is the direct competitor to LocalBitcoins. After LocalBitcoins has been shut down this is the service to go.

However, I wonder why people still exchange Bitcoin in face-to-face meetings today. That would be far too dangerous for me given the value of Bitcoin. Personally, I wouldn't meet up with a stranger to exchange Bitcoin, as it can be assumed that you are carrying a lot of money with you. Even in public places, such an exchange is no longer safe these days. In the past, when Bitcoin was worth much less and you could exchange small amounts, it was different.

[1] https://agoradesk.com/