This question seems, to me, to make a couple of assumptions about the Norse diaspora that aren't well-founded - specifically the terms "conquered" and "home".

Conquest is a difficult framing for much of the Norse expansion in the 9th and 10th centuries. While a strong argument could be made that the so-called "Great Heathen Army" in the second half of the 9th century can be described as a conquest, given that 1) whole families came over from Scandinavia and 2) parts of the early English elite were replaced by either elites chosen by the Norse or were replaced by Norse warrior-elite entirely, it is not unproblematic - we don't have primary written evidence by participants in the GHA to indicate that anyone actually thought about it as "conquering" new land! However, this framing becomes much more problematic outside of the British Isles:

• Iceland was known to be more-or-less uninhabited by the beginnings of the landnám of that island, meaning there is land to claim, not nothing to "conquer.
• The ceding of Normandy to Rollo/Hrolfr shouldn't be interpreted as conquest - he had been raiding for a long time in Frankia with no permanent bases. Norse raiders either negotiated with villages for supplies or established overwinter camps, but what settlements had been founded by Vikings disappeared in the early 10th century. This makes it appear less like a continuous, successful conquest, and more like an opportunistic way to get access to the resources, particularly salt, that they had already been raiding for for many years. The same goes for the rest of Europe - there are very few long-term settlements outside of the North Sea area.
• The origins of Scandinavian elite in the Kieven Rus' is uncertain - the most widely accepted theory is that traders from central Sweden made up the first contacts in eastern Europe, and warriors joined them later. They do have a fairly well-developed series of settlements, though, and become the initial elite around Novgorod in a predominantly Slavic area, so it is plausible to interpret it as a "conquest", but one that results in a hybrid culture independent from mainland Scandinavia.
• The far-distant places like Constantinople, Morocco, or Vinland cannot be described as conquest - while Constantinople was attacked in 860 by Norse people and later had the Varangian Guard, and Vinland had a settlement that intermittently occupied for somewhere between 14 and 150 years (recent soil-pollen archaeology indicates a much longer period of use at L'anse aux Meadows than the saga sources do) , neither of these exerts a significant degree of control over the landscape or society, and so can't be framed as conquest.

"Home" is also not as straightforward a term as expected. Saying the "Vikings" had a home, even though I can safely assume you mean mainland Scandinavia, assigns a homogeneity to Norse people in the Viking Age that was by no means present. Intra-Scandinavian conflict, initially between petty kings locally and later by the slowly forming territories of Norway, Denmark, and Sweden, was constant, and many raids were inflicted on other Norse peoples. As such, someone living on Lofoten and someone from Uppsala have fairly dramatically different cultures, customs, and language, and where they would have chosen to raid was different! Sweden tended to raid in the Baltic to the Caucasus, while Norwegians and Danes tended to travel south and west.

So, all that being said.... to directly answer your question - assuming conquest means the replacing of the elite and the establishment of long-lasting settlements, the farthest away would be the Kievan Rus', centered on the Volga and Dnieper rivers. If we expand the term to be anywhere that Norse peoples raided, though, then we have contemporary runestones recounting an expedition led by one Ingvar from Sweden to "Serkland" in 1041, which may refer to Persia! As such, Norse peoples in the 11th century travelled to half of the Northern Hemisphere, a truly remarkable diaspora even though most of that contact did not lead to permanent settlement or conquest.