First of all, keep in mind that not much changed between, say, 1800 and 1805. So if you want just general stuff, you can generalize. Example:
In this first decade of the new century American schools changed little from the schools in the late eighteenth century. Education was still considered mainly a family or local responsibility, not an obligation of the state... Schooling was conducted in the home or in small, one-room school houses. The curriculum centered on the "3 r's" along with moral and religious training. The purpose of learning to read was to be able to read the Bible for oneself. Dame schools, provided for a fee by women in their homes, taught the alphabet on a "hornbook" . Sometimes citizens of a local community would band together to hire a teacher to instruct their children. The teacher, usually a man, would be paid little, often have only a rudimentary education himself, and be boarded at a home in the community
In this country founded on freedom of religion, most printed music in the early 1800s was religious in nature, including Amazing Grace and Coronation. Episcopalian Harmony Evangelical Harmony, and Plain Psalmody were typical of the first books printed. Americans also enjoyed singing old English ballads like Greensleeves and Scottisk folk tunes such as Froggy Went A-Courtin'. Most country folk used tuneless word books and sang the words to known tunes.
In the first decade of the 19th century, Americans dressed, prepared their food and furnished their homes much like they had in the late 18th century. Women usually wore long flowing skirts, a blouse with a low neckline and a separate half-blouse with a modest high neckline (worn under the low neckline blouse). Hats and shawls were stylish accessories that were necessary in cold weather. Shoes were not made for comfort--a shoe could fit either foot!. Women prepared food for their families, using simple cooking utensils, from food they grew in gardens. Many American homes had furniture that was painted and decorated with French and English designs.
Religious freedom helped create denominations other than the well-established Presbytarian Church. Congregationalist and Presbytarian churches, which were very strong in New England, met competition from Lutherans, Methodists, Methodist Episcopalians and Baptists.
More specific things:
1800: End of the Quasi-War ((http://en.wikipedia.org/wiki/Quasi-War)
between the U.S. and France (it started in 1798).
In 1800 a movement to reduce the influence of the Bank of the United States (which had opened in 1791) resulted in the creation of state banks throughout the country.
The Library of Congress was established in 1800 with a $50,000 appropriation to purchase 900 books and maps that arrived from London in eleven trunks.
(The novel was just beginning to be popular. William Hill Brown (The Powers of Sympathy) published the first American novel in 1789 and between that time and 1800, there were 350 novels published. Women particularly loved reading. This process improved women's literacy and encouraged them to think for themselves. The Coquette by Hannah Webster Foster, had become the first best-selling novel - just before 1800. Historical writing became popular during this period as well. David Ramsay published The History of a Revolution of South-Carolina and a biography of George Washington. Another biography by Mason Locke Weems which included the famous cherry tree "I can not tell a lie" story glorifying Washington was so popular that it went through 40 editions in 25 years.)
Noah Webster published the American Spelling Book around 1800.
Massachusetts led the way in public financing for education. In 1800 its legislature gave local school districts the power to levy taxes.
Thomas Jefferson won the 1800 presidential election ((http://www.presidentelect.org/e1800.html)
The Indiana Territory was created. ((http://www.in.gov/history/6214.htm).
In 1800 to 1809, Napolean commissioned Robert Fulton, an American artist who was then living in France, to build a submarine. Using Bushnell's design, Fulton built and successfully tested the submarine, but interest waned as the French decided that such a sneaky attack was ungentlemanly. Fulton's interest turned to steamboats.
Late in the eighteenth century and early in the nineteeth century, the Second Great Awakening began. The first great awakening consisted of religious revivals that had occured during colonial settlements. Similar camp meetings helped promote the Second Great Awakening. The first of these camp meetings took place in July, 1800 at Gasper River Church in Southwestern Kentucky.