I know Belfast seems like an obvious choice but we'd be looking somewhere quiet with no pushing and shoving.
I don't bother with Belfast much so don't know where would be suitable, and if I do go in I catch the airport bus and don't bother with the car.
If most were driving might it be best to pick somewhere in the outskirts. With the motorways and ringroads it's nearly easier to cross the city than go into it..
I'll go anywhere but as an example, there is Corrs Corner just off the M2 at Glengormley with plenty of parking. Hotel and restaurant. They serve all day i.e. morning coffee, lunch. afternoon tea. Plenty of seating. And it would be easy to book a table, or a couple of tables put together, for coffee/scones/whatever.
It happens to be on my side of the city outskirts but I'm just using it as an example. Perhaps that type of place rather than jostling in the city centre.
Just an idea to throw into the ring.