For the first immigrant known in the line you are researching, make a "cluster" list. This is a list of all people he is known to associate with; in business, church [never ignore one's religion], politics... You get the idea. Then you research these individuals. Find out when they arrived in the same area as your ancestor; maybe your ancestor traveled with some of these "cluster" people. People generally did not travel without a "support system" in place; either coming along with them, or already in place at their destination. This is a time-consuming process, but can be VERY rewarding.
In checking the ship immigration list, don't look at just the obvious. Try to think in broad terms. Immigrants often "stopped over" on their way to their real destination. Check all those possible places/immigrant lists as well. Check every possible derivation of your surname, making notes and documenting sources for EVERY one. And keep it all organized. Here is an example of when a situation demands keeping an open mind:
My Logan line had been "stuck in America" since the first known family history was written in 1829. At that time it was stated that our first immigrant [Col. George Logan] came to Charleston, SC in 1690, and was from Aberdeen, Scotland. I now know this is true, but by no means the WHOLE story. With the details left out, I could not make "the leap across the ocean". Here is what was missing: Col. George Logan's parents moved from Aberdeen BEFORE George's birth. George was born in Westminster, England. When George migrated to South Carolina, he did not come directly there. He stopped and set up his business contacts and married a girl from Barbados. The only way to discover this missing information was to develop a "cluster" for George and check out everybody. What it told me was: he was Scots by birth, but lived like English gentry. Not what you would expect from an Aberdeen immigrant! But exactly what you would expect from one born and raised near London. Mystery solved!