Is the LDS observance of the Sabbath on Sunday based on revelation? Is there modern revelation as to the day of the week where we should observe the Sabbath? I hear that in countries where saturday is the official day of rest, church meetings are held on saturday. So, is there some revelation stating the day of week we should observe the Sabbath, and this is an exception, or is it revealed that the exact day doesn't matter too much, as long as it's every 7th day?

So, in essence: Do we meet on sunday because everyone else does it, or is there actual doctrine regarding when we should meet?
According to fairmormon.org:


  Latter-day Saints do not base their worship practices on an analysis
  of early Christian history, or on the comments of scholars in Biblical
  commentaries, though these sources can confirm Church teachings.
  Rather, the Saints follow the guidance of a living prophet. However,
  it seems clear that the Latter-day Saint practice of observing the day
  of rest and worship on Sunday—like most of the Christian world—is
  consistent with the earliest Christian practice of which we have
  record. 


See Brian's answer


  Interestingly, however, the most important aspect of Sabbath worship
  for the LDS seems to be the worship, and not the day on which it is
  held. Most LDS worship occurs on Sunday. General Authorities, who must
  often travel on conference assignments on Sunday, fast and receive the
  sacrament weekly on Thursdays. Church branches in Israel worship on
  Saturday. Branches in Muslim countries, such as Egypt, meet on Friday,
  the Muslim holy day. Wrote one account of the Church in Israel:
  
  Jerusalem is home to three major religions: Judaism, Christianity, and Islam. None of the three shares the same day of worship. Islam
  recognizes Friday as a holy day, Judaism celebrates the Sabbath on
  Saturday, while Christianity generally adheres to a Sunday day of
  worship. These differences posed significant challenges in the lives
  of the Saints living in the Holy Land, and David Galbraith posed
  questions regarding this matter to President Lee during the Prophet's
  visit to Jerusalem [in September 1972].
  
  Following President Lee's visit, branch president David Galbraith wrote a letter to the First Presidency wherein he outlined four major
  concerns and formally recommended that the day of worship for
  Latter-day Saints in the Holy Land be changed. The four concerns were
  as follows: First, for the Jews, public transportation ceases on
  Saturday, stores and places of entertainment are closed, and in
  Jerusalem the streets are full of families going to and from their
  synagogues. Second, Sunday, on the other hand, is a normal working
  day. Those attending the universities have classes, many of the
  children have school, and, in fact, everyone except those in the
  diplomatic corps have other obligations on that day. Third, the
  members were scattered throughout the country, and the majority relied
  on public transportation. It would be impossible to hold late
  afternoon or evening services on Sunday. Fourth, the members of the
  Church had been holding their meetings on the Jewish Sabbath rather
  than Sunday for some time with at least the tacit approval of the
  mission.
  
  Two months after President Harold B. Lee's visit to the Holy Land, he authorized President David Galbraith to conduct worship services in
  Israel on the Jewish Sabbath (Saturday). This authorization is dated
  November 20, 1972. This decision in Israel served as a precedent to
  include Friday observance as a day of worship in countries of
  primarily Islamic populations, such as Egypt and Jordan.


Note that this is not an official source, but I have no real reason to doubt that this event happened as reported.

To finish, it seems like there is no clear commandment in Doctrine and Covenants to hold the sunday as Sabbath, but we do hold the sunday as Sabbath because the prophets have taught us so - and it seems to be consistent with the NT, or in other words, that has been the prophets' understanding of the scriptures so far (see Brian's answer).