Before the 20th century most people tended to stay close to where they grew up.This was partly because travel was difficult (lack of bridges across rivers and so on), but also because if you stayed put, you would have an entire support network of relatives nearby - useful in hard times.
There were exceptions of course - priests would frequently be assigned to a church in a different part of the country than where they grew up...and they would get a local wife (or a mistress in Catholic times) and raise their family there.
Also, in the 19th century you would have large groups of men moving from the rural areas to the seaside during the fishing season, and some of them would settle there permanently.
In the 20th century things got mixed up a lot and most people today will have ancestors all over the country.Take myself for example - my grandparents were from Breiðafjörður (West Iceland), Blönduós (North Iceland), Rangárvellir (South Iceland) and the area near Mývatn (North-East Iceland).They, or their children moved to Reykjavik, where I was born.This is quite typical for the current generation.
Now, my advice is that you should go to the Ljósavatn area primarily for the purpose of seeing the old farm sites and such - it is possible that the people there are closely related to you, but it is not very likely.
Alternatively, if you can tell me who your most recent Icelandic ancestors were, I can just check for you in the database where their closest living Icelandic relatives are today.