Before the king's were thrown out, how big was the Roman regions?
There is no direct evidence, but from indirect evidence we can surmise that by the end of the regal period (roughly the end of the 6th century BCE), Rome was the most powerful and most culturally important city of Latium. Estimates of the city's size usually hover around the low 10s of thousands. 20,000 seems about right, with the ability to put somewhere between 5,000 and 7,500 soldiers in the field--one consular legion, or two understrength legions under two consuls. Such a force was probably superior to that of any Latin neighbor, and on par with what the major city-states of Etruria could muster at the time. This population figure is weakly supported by the city's apparent urban footprint, which was apparently quite large given the time period. This population advantage was probably due to Rome's position at an important crossing of the Tiber, which facilitated communication between Etruria to the north, Latium, and the Greek cities of Campania to the south. Early evidence suggests Rome was already a mixture of Latin, Etruscan, and Sabine populations (see reference below).
By land area, some (very rough) archaeological data suggests a territory of about 800 square kilometers, and much of it controlling access to and crossing of the Tiber. This was the largest of the cities in Latium, comprising about 35% of the whole of Latium. Her closest rivals in size were Tibur, Praeneste, Ardea, Lavinium, and Lanuvium (all present on the linked map). Very soon after the end of the regal period, Rome effectively annexed Crustumerium (up the Tiber to the northeast on the map), which greatly increased her size relative to the other city-states. And of course Veii would be a major rival to the north until eventually defeated.
For more discussion of Rome's size and cultural position at the end of the regal period, see Forsythe, A Critical History of Early Rome (UC Press, 2005), beginning p.115.