Does the Old Testament foretell the time in history in which the Messiah would come (the first time)? I understand that the Old Testament prophecies many different things about the Messiah who was to come, including the virgin birth, His suffering, His resurrection, etc.  

However, is there anything in the Old Testament that indicates the time in history in which He would come, or is it just "some time in the future"?
Yes. Daniel, who wrote during the Babylonian Empire prophesied that Messiah would come after four succesive Kingdoms. One which had already existed, the Babylonian, would be taken over by the Persian, then the Persian taken over by the Greek. The Greek then taken over by the Roman, then Messiah overthrowing the Roman. This is not just a Christian re-interpretation but an actual Jewish expectation that Messiah would overturn the Roman Empire.  Of course the common Jewish expectation was that Messiah would lead by sword, not by conversion to an 'invisible' kingdom, but nevertheless, both traditional Jewish and Christian interpretation of Daniel Chapter 7 puts Messiah after the formation of the Roman Empire.

A wiki article on the four beasts of Daniel has it right:


  The following interpretation is a traditional view of Jewish and Christian Historicists, Futurists, Dispensationalists, Partial Preterists, and other futuristic Jewish and Christian hybrids, as well as certain Messianic Jews, who typically believe that the kingdoms in Daniel (with variations) are:



Neo-Babylonian Empire 
Medo-Persian Empire
Macedonian Empire of
Alexander and his successors to the Ptolomaic and Seleucid Empires
together, and
Roman Empire, with other implications to come later.


This was the scheme described by Jerome in his Commentary on Daniel.[7] Within this framework there are numerous variations.

Yet this is not all. Many respectable theologians believe that Daniel was more particular in foretelling the time of the coming of Christ than ever any prophet had been before. In Daniel 9 of his prophecy, it is foretold that it should be '70 weeks', i.e. 70 weeks of years, or 70 times 7 years, or 490 years, from the decree to rebuild and restore the state of the Jews till the Messiah should be crucified. There is much calculation by various people to argue that this was the very year that Christ died dated from the commission granted to Ezra by Artaxerxes in Ezra 7. Naturally this is fairly complicated to prove and there would be much debate about the details.

However this exactness to the precise year does not appear to have provided any Rabbinic traditions to expect Messiah at the time of Christ exactly, rather according to the Jewish historian Alfred Edersheim there was many guesses from around 4000 years after the Creation to around 729 A.D. based on an extended view of a five monarchy prediction where after Rome somehow Ishmael was added without any scriptural warrant. Yet even in this confusion and speculation some interesting Rabbinic opinions can be found concerning Daniel. First around the time of Messiah as predicted by Daniel some thought that the second temple would be destroyed which is surprisingly accurate considering. 


  Dan. 9:24. In (The Talmudic Tractate Nazir, on the Nasirate. 32 b) it is noted that this referred to the time when the second Temple was to be destroyed. So also in Yalkut vol. ii. p. 79 d, lines 16 &amp;c. from the bottom. (Edersheim, A. (1896). Vol. 2: The Life and Times of Jesus the Messiah (P734)


Second, a kind of disappearance and reappearance of Messiah was thought of. Although not seen as 3 days in the grave a 45 day disappearance is again a pretty good guess:


  Dan. 12:11, 12. These two verses receive a peculiar Messianic interpretation, and that by the authority of the Rabbis. For it is argued that, as Moses, the first Redeemer, appeared, and was withdrawn for a time, and then reappeared, so would the second Redeemer; and the interval between His disappearance and reappearance is calculated at 45 days, arrived at by deducting the 1,290 days of the cessation of the sacrifice (Dan. 12:11) from the 1,335 days of Dan. 12:12 (Midr. on Ruth 2:14, ed. Warsh. p. 43 b). (Edersheim, A. (1896). Vol. 2: The Life and Times of Jesus the Messiah (P734).


These predictions are all quite remarkable and they shows us how precise and speculative those were who pondered them, yet somehwat accurate still. Also it should give us pause to consider how miraculous that these prophecies did predict events which arguably occured. Of course after the fact we are able to see the predictions more clearly but that is partly the purpose of prophecy, to prove that events which have occurred were clearly predicted by an omniscient God.