About that 1630 claim
White's states plainly that it is the oldest tavern in Belfast, established in 1630, on the basis that the first tavern licence granted in the town went to the building where it now stands. That is the claim on the wall and on the website, and it is repeated widely.
It is worth knowing what is solid and what is not. The 1630 licence is the earliest recorded grant of its kind in Belfast, and the location is right. What is not documented is a surviving building from that date. The structure you walk into today dates from the late 18th century, when the earlier premises were demolished and rebuilt by Valentine Jones. Local history researchers have pointed this out for years.
So the honest version is this: a licensed house has stood on this ground since 1630, and the walls around you are Georgian rather than Jacobean. That is still a remarkable run of trade on one spot, and it does not need embellishing.
The entry itself carries the rest of the story. From the 1600s into the 1700s the alley was lined with wine and spirit merchants, which is exactly how Winecellar Entry got its name. The Belfast Mercury newspaper was founded down here in the 1850s. You are standing in a working lane of the old town, not a reconstruction of one.