One of the first things to attempt is to theorize what caused a possible migration in the first place. For clues to this answer, one of the most fruitful places to check are local histories. One of the major driving forces of migration is economics, so consider your ancestor's occupation. If he was a farmer, were there crop failures or droughts in the area at the time you think that he might of left? Sometimes farmers left simply because the soils in their area had become exhausted from many years of crops. If he was employed what was happening in the industry that your ancestor worked at that time? Another factor that is often not recognized is that people moved to escape illness and plagues. Land was also a big incentive for movement. The Homestead Act of 1862 encouraged many people to move westward. Men also moved to claim military bounty land. Other reasons include religious persecution and moving to follow friends and family.
Once you have determined why your ancestor may have moved, find out what means they may have used to travel. What were the common migration routes in that area? Don't forget to explore the possibility of canal or river travel. Once you find the the most likely route of travel, which will probably be the closest in proximity to your ancestor's home; you can research to determine where these routes lead. One technique that might help you to theorize where your ancestors went is to research along those routes of travel to see where your ancestor's occupation was flourishing. Checking census records of surrounding areas may prove fruitful.
Another useful technique is to research what regions of the country experienced population surges around the time that your ancestor disappeared. Kentucky saw a huge growth in population between 1790 and 1800, nearly tripling its population from 61,000 to 179,000. Under Virginia law, older sons inherited their father's lands, which forced younger son's to look elsewhere for land, often to Kentucky and North Carolina.
You will test and exhaust many theories in attempting to find disappearing ancestors, but part of the fun of genealogy is the elusive nature of people. Everyone loves a mystery and we each have generations of them waiting to be discovered.