The largest city in the Americas in AD250 would be the city of Teotihuacan in central Mexico. Map of the city here.

The 3rd century is when Teotihuacan reached its apex and the size of the city population probably exceeded 100,000 people. Partially this was due to the eruption of the Xitle volcano in the valley of Teotihuacan that erupted in the second half of the 3rd century. This eruption, which left Teotihuacan largely unharmed, probably resulted in huge refugee populations joining the city and staying for good.

In terms of area, the city at maximum size would have covered about 8 sq. miles or about 20 sq. km. The city probably wouldn't have covered its maximum area yet in AD250, but the high level of urban planning involved in building the core of the city means it probably wasn't too much smaller at that point in time than its maximal size.

In short, a population of more than 100,000 and an area of around 20 sq. km.

As for comparison with Rome, I can't give any authoritative information, but perhaps /u/Tiako or /u/XeonophonTheAthenian can give you that information.

Source: Evans, Susan Toby 2004 Ancient Mexico and Central America: Archaeology and Culture History. Thames and Hudson.