'City' isn't really the right term for these Norwegian sites. Nidaros had just been founded as a cathedral and (as Wikipedia calls it) a 'palace' in 997. To me, this suggests a pretty dispersed site, probably with one exceptionally large farmstead located close to a church, which would have been surrounded by dorms for monks and smaller farms for the lay people who did a lot of the daily work for the church community. This is, at least, probably what Gamla Uppsala looked. There's no way to give a precise estimate of population, but I would guess that this settlement pattern could sustain 300 or 400 people, spread out within about an hour walk from each other.

That said, this small population could act as a magnet for travelers from other regions, occasionally expanding due to religious festivals or royal assemblies. This probably would have looked a lot like the Althing in Iceland, with small encampments spread across the area and regular gatherings for public events. It's possible that these kinds of events could have attracted hundreds of travelers, pushing the area population above 1000.

Tønsberg was probably much more modest, perhaps just one or several important farmsteads. The Vestfold region was very wealthy throughout the early Viking Age, with massive burials at places like Gokstad and Oseberg testifying to the presence of social elites and the town of Kaupang attracting a population of perhaps 1000 merchants and craftsworkers. However, it looks like Kaupang went into decline around the year 900, and there are few burials of the same extraordinary wealth in late Viking-Age Vestfold. The area remained agriculturally important and well-connected by both land and water, but there don't seem to have been any major population centers. Tønsberg, assuming that it was an important farmstead, probably consisted of several buildings and perhaps a few satellite farms. Overall, I'd estimate a population of no more than 100 to 200 people.

The biggest city-like places in Scandinavia during the Viking Age had been Kaupang (ca. 800-900), Hedeby (ca. 800-1050), and Birka (ca. 800-1000). These settlements probably had over 1000 permanent inhabitants, and few reasonable estimates would place their populations over 2000. They disappeared at the end of the Viking Age, however, and were replaced by a new set of sites—places like Bergen, Schleswig, Sigtuna, and Lund. I'm less familiar with the archaeology and history of medieval Scandinavia, but these towns seem to have been smaller. Lund and Sigtuna, I suspect, began with a population of perhaps 400 to 600 people. These were primarily religious and trading sites with some specialized production, such as coin-making. By the later Middle Ages, these sites probably boasted 1000 people, and maybe even more, but again, I think they're still imagined more as regional magnets than massive population centers.

I hope that helps! These kinds of questions are difficult to answer, since we don't have actual population records, and making population estimates based on partially-excavated sites—often heavily disturbed by later urban development—is tricky business.