Introverts = Cafe or Teahouse
Ambiverts = Bistro or Izakaya
Extroverts = Bar or Club
These places have some food on the menu, so no need to go to a restaurant to eat. The main objective is drinking, alcoholic or non-alcoholic you will decide.
Avoid the super posh fancy restaurants on the first date, the 'family-friendly franchise' restaurants you also avoid as you do not want brats to ruin the atmosphere, especially during the school holidays.