You may be interested in reading this earlier answer of mine to a similar question. There, I detailed the timeline for the disputed 1800 election, and the undisputed landslide election of 1808.

To summarize that answer, in the early 1800s, news would take between one and four weeks to reach most of the U.S. population, except for those people who lived very remotely, on the frontier or otherwise isolated from a wider community. Within six weeks, if a person was interested in hearing the news, and they lived somewhat near an actual town or along a river or mail route, even in the rural back country, then they almost certainly could have heard it.

That previous answer deals with the 1800 and 1808 elections. The 1800 was contested between Thomas Jefferson and John Adams. So, while most people would have understood by mid-December 1800 that John Adams had lost, the contest between Jefferson and Burr was not actually settled until February 17th. Washington, D.C.-area locals likely heard that same day, and those in Virginia and Maryland who were within a day's stagecoach-ride or boat-ride would have heard the following day. Everybody else, it would have been longer, but still, most people would probably would have known the results within a week of Jefferson's inauguration on March 4th, if not sooner.

In the 1808 election, it was a landslide for James Madison, and newspapers were projecting him the winner in early November. These projections were confirmed as more election returns trickled in, and by mid-December, most newspapers were considering him the President-Elect.

Going forward in time, the results of the 1824 election were not known right away, because nobody won the Electoral College outright. Just as had happened in 1800, the election was thrown to Congress, which was being reported in newspapers as the outcome by December. The election was settled in Congress in mid-January, so most people would have known by mid-February, and only the last stragglers wouldn't have known by Inauguration Day.

By then, transportation infrastructure had gotten better—stagecoaches and steamboats could carry the news with some speed. And it continued to get better from there. The 1828 election—a landslide for Andrew Jackson—was called for Jackson almost right away. As an example how (relatively) quickly the news spread, by November 15, 1828, the weekly Indiana Palladium newspaper in the rural town of Lawrenceburg, Indiana, projected that Andrew Jackson had become President-Elect:

"As the case now stands, there remains no doubt of the election of General Jackson, by a large majority of electoral votes. The following states may now be considered as sertain [sic] for the General..."

After listing the Jackson states and their respective electoral vote totals, the Palladium concluded that this made an aggregate of 147 votes, "a clear majority of the states. If this estimate be correct, it will appear that Jackson is elected without the aid of another state, 131 only being necessary for a choice."

In the following weeks, the newspaper would re-affirm this projection, adding new states to the "certain" column for Jackson, or for Adams.

From the 1840s on, the election results were pretty immediate, due to steamboats, railroads, and beginning in 1844-48, the telegraph. The elections were predicted within a week of Election Day in early November. Take the New York Herald's reporting of the 1840 election, for example. Polls closed in New York on November 5th. The Herald had already been reporting some of the election returns from other states that held elections earlier. Then, on November 5th and 6th, they could publish nearly full returns for PA, and partial returns for CT, RI, OH, NY, NJ, NH, MD, ME, and VA. Based on the returns they had, on November 6th, they predicted William Henry Harrison had won ME, RI, CT, NJ, and MD, while Van Buren had won NH. PA was still "too close to call". (The Herald reported that both parties were claiming victory in the state.) They also project NY as going for William Henry Harrison, and so he "has the majority of the Union. HE IS THE NEXT PRESIDENT OF THE UNITED STATES. HURRAH!"

The next day, though, they reversed course:

"ASTOUNDING INTELLIGENCE. PROBABLE RE-ELECTION OF VAN BUREN. PROBABLE DEFEAT OF GEN. HARRISON."

This was based on further returns that had come in, that showed that Van Buren might carry New York. But then just a day later, on November 8th, the Herald reversed themselves yet again:

"GREAT VICTORY. GENERAL HARRISON GETS NEW YORK, AND IS ELECTED TO THE PRESIDENCY."

They stuck by that from there on out, and with more returns over the next week, Harrison was President-Elect.

Four years later, with the telegraph infrastructure much more comprehensive, the New York Herald could make quite precise predictions in short order. The day after Election Day in New York (and most states), on November 6th, the Herald ran the headline: "Nothing more Likely than that POLK IS PRESIDENT". They could only report the likely outcome of four states that day, though, but projected several others. Over the next nine days, they published a table of results, based on the returns that had come over the telegraph and otherwise, listing states as "Certain" or "Probable" for each candidate, and the states that remained "Doubtful" (i.e., too close to call). On November 15th, the "results received" allowed them to declare Indiana "Certain" for Polk, which put him over the top. The following day, they moved Missouri into the "Certain" column for Polk, and the paper declared Polk the winner: "As Polk is the President elect beyond all doubt, we shall not publish any more details till the official returns are received."

1848 was even faster. The day after Election Day in New York (and most states), on November 8th, the paper projected Zachary Taylor had won, under the headline "The Probable Result". They moved more states into the "Certain" column for Taylor the next day. And then the day after that, on November 10th, they reported that Taylor had certainly won 160 of the 163 electoral votes needed to win, with eight states yet to report their totals, and several of them projected to go to Taylor. "It appears, therefore," the paper wrote, "that [even] without eight States that are yet to be heard from, Old Rough and Ready [Zachary Taylor] has been elected, and has fourteen electoral votes to spare." This was confirmed the following day.

Even in the rather contentious election of 1860, both the partisan rivals the New York Herald and the New York Tribune declared Lincoln the winner the morning after Election Day. News may have even been circulating the previous evening. In South Carolina, the state legislature held a special session a day after that, in responde to Lincoln being elected. They passed a bill declaring their intention to secede, citing Lincoln's election. So obviously the news was traveling fast. During those days, the New York Tribune was reporting on developments in the South, including speeches and votes, within 24 hours of them happening.

So, the elections that took the longest to know the results were the elections before 1840, particularly the ones where there wasn't a sure winner right away. Even as early as 1808, landslides could be projected in the first half of November. After 1840, election results were essentially known, and not just projected, within a couple days of the election. The only exceptions were the elections where the results were in dispute - 1876, and 2000 being the only notable exceptions. Even in the close 1948 and 1960 elections, it was only a day later, at most, that the winner was declared by most news outlets.

cont'd...