I've done some research, but population figures have been unspecific. I've seen the 1 million figure around, though I'm unsure if it refers only to the population within the Aurelian Walls, or the population inside and outside of them (if anyone even lived outside them). Could anyone give me a reliable figure or maybe point me in the right direction?
The estimates of Roman population, and the areas covered are difficult to pin down. One of the best sources I have looked at is The Cambridge Companion to Ancient Rome By Paul Erdkamp. He explains a lot of the difficulty in nailing this figure down.
This book, in pages 32-35 goes into details on the area covered-and the discrepancy between the area contained by the Aurelian Walls and the areas defined as Rome by Augustus in his 14 regions, and discusses population densities derived from possible building types, areas, and occupancy.
Estimates can be derived from the number of domus(1790) and insulae(46,500) that were recorded as existing in Rome by the Regionary Catalogues, and again estimating the number of people occupying each.
Depending on how many occupants each building had, and the area each insulae covered, you can get population densities anywhere from 10,000 to 70,000 people per square km, giving possible populations anywhere from 230,000 to the often quoted 1 Million.
Reconstructing Italy: The Ina-Casa Neighborhoods of the Postwar Era, p. 133 states that the population of Rome in 1870 was 230,000. This book also makes the (unsubstantiated) claim that the population under Augustus Caesar was 1,000,000.
This was the population inside of Aurelian's Wall, which had delimited the City of Rome from Aurelian's reign, begun in 270 AD up until 1871. Discarding the Augustan guess-timate, often repeated, of 1,000,000, the population was certainly less in 270 AD than it had been in the early days of the Principate: we are in the latter days of the era of "Military Anarchy", 235-284 AD.
During this period the Empire suffered "invasion, civil war, plague, and economic depression." Populations declined across the empire, including at Rome. Aurelian responded by increasing the dole of free food at Rome, which may have increased or at least supported the population of the city.
In 286 AD the Emporor Diocletian moved the western capital from Rome to Mediolanum (Milano), which reduced the importance of Rome, and removed most of the military, and many of the civil bureaucrats from Rome. As a result, the population of Rome began to shrink. It is often estimated at 50,000 in the late middle ages.
Thus starting with a possible maximum population of Rome and immediate surroundings of 450,000 during the early Principate, a minimum of 50,000 during the late middle ages, and increasing to 230,000 by 1871, we have not yet found an academic estimate for the population of the city during the period 270 AD and following.
My guess is that Rome had already declined to a population of under 200,000 by the time of Aurelian, and thereafter declining until growth resumes in the late middle ages, and increasing steadily until it reaches 230,000 in 1871.
The "Atlas of World Population History", by Colin McEvedy and Richard Jones, 1978, Penguin Books, gives the maximum population of Italy as 7 million, peaking during the first two centuries AD, during the Pax Romana. It declines to 5 million by 400 AD, and sinks to 3.5 million by 600 AD, it's lowest value. The decline during the 3rd century AD is due to the reverses of the Roman Empire, and the City of Rome will be taking many of those losses, as it is an "Imperial Parasite", feeding off of the entire empire.
Thus the answer to your question is: it was at it's largest under Aurelian and his immediate successors, but thereafter in decline; the largest population ever recorded while Rome was delimited by Aurelian's Wall was the 230,000 enumerated in 1871.