All US Coins were minted at Philadelphia until 1838, so a coin from 1800 won't have a mint mark.
The first branch mints opened in Dahlonega, GA and Charlotte in 1838 to strike gold coins using metal from nearby mines.
It depends on the type of coin the date and denomination on were the mint mark is located
The mint mark is located on the reverse [tails] side of the coin at the bottom below the wreath. If there is no mint mark then the coin was minted at the Philadelphia Mint.
The lack of a mint mark usually indicates that the coin was minted in Philadelphia.
The letter is known as the mint-mark and tells where the coin was made. A coin having a P mint-mark (or no mint-mark on some coins) was made in Philadelphia, a coin having an S Mint-mark was minted in San Fransisco, a coin with a D mint-mark was minted in Denver.
It can only be on the front, back or edge of a coin.
Please post a new question with the coin's exact date. The New Orleans Mint operated for many years and "1800's" isn't specific enough to ID a coin.
A mint mark tells where the coin was minted, for example, a P mint mark (or in some cases no mint mark) signifies the coin was minted in Philadelphia, D is for Denver, S is for San Fransisco. I'm assuming someone told you that the mint mark was under the eagle for whatever coin you had, so you simply need to look under the eagle to find a mint mark. Keep in mind that some coins were produced in the Philadelphia mint and have no mint mark.
Normally you have to know a coin's denomination to locate the mint mark because it can be in different places. Also, Philadelphia did not use a mint mark on most coins until 1980 so it's very possible your coin doesn't have a mint mark. Once you know the denomination you can check a site such as www.coinfacts.com that shows the mint mark locations for all US coins.
There is not always a mint mark on coins. If your coin does not have a mintmark it means that it was made at the Philadelphia mint in Pennsylvania.
No US coin bears an "F" mint mark
Mintmarks identify which mint the coin was made at.
The mint mark of the Denver Mint (shown as a "D") and the San Francisco Mint (shown as "S) on the Eisenhower Dollar is located on the obverse (heads) side of the coin directly beneath the bust of Eisenhower. If there is no mint mark there, then the coin was struck at the Philadelphia Mint and in this mint did not place a mint mark on the coins struck there until 1979.