In "The Council of Elrond" Boromir states that he has journeyed one hundred and ten days to reach Rivendell from Minas Tirith. Why did it take him so long? Gimli states that Mordor to the mountains above Moria is 300 leagues which is 900 miles (when they are contemplating the Redhorn pass). Minas Tirith is a bit nearer, but they've travelled south from Rivendell so I estimate his journey at 1000-1100 miles. So at best he's averaged 10 miles/day even though he's a strong determined man on horseback. I just can't reconcile that journey time with the known dimensions of Middle Earth.
There were a couple of reasons. Firstly, as jwenting states, he simply didn't know where it was. As he said at the Council of Elrond:
Long have I wandered by roads forgotten, seeking the house of Elrond, of which many had heard, but few knew where it lay.
The second reason is that he lost his horse halfway through, as he tells Celeborn:
A long and wearisome journey. Four hundred leagues I reckoned it, and it took me many months, for I lost my horse at Tharbad, at the fording of the Greyflood.
(Note that the comparison to the distance from Moria is not very useful: Boromir did not go that way, but went via the Gap of Rohan, as Saruman had not yet revealed himself as a traitor. However, all things being equal, that would actually have shortened his journey, if not for the points above.)
The main reason as stated in the books is that he didn't know where it was. He had only an old riddle to go on, which told him to seek out Imladris, where Elrond Half Elven dwelt.
Not only was that name almost forgotten, the location was too. So he spent a lot of time wandering whither and thither looking for information about Imladris, until eventually arriving there.
In the essay on the Palantíri in Unfinished Tales, we are told that the palantír of Minas Tirith was designed to interact most with the palantíri of Gondor, of which only three remained: one in the hands of Saruman, the other controlled by Sauron. Only a strong will and the right to use them enabled Aragorn to wrest the stone of Orthanc from the will of Sauron. Presumably Denethor started using his stone before the return of Sauron and would have been free to turn his attention wherever he wanted, but his interest was Gondor and its enemies, not distant Elvish realms which were probably screened by the power of Vilya the Elven Ring. He may have conversed with Saruman, a similarly proud individual.
However, Sauron would change all of this; he exerted control over what the other two keepers of the Palantíri could see, which was largely images of his huge armies gathering to overwhelm all opposition. He may have stopped them conversing with each other. By that time Denethor would realise that trying to look at Imladris would draw the Eye there. He was not happy about sending either of his sons on the quest; only Boromir's stubbornness saw the quest happen at all.