Columbus was quite a well-travelled man by the time he started his grand project of reaching the Indies sailing Westwards, but it's hard to know with complete precision how much he had travelled.
We know for certain that he lived in Lisbon for some years until he became a widower in 1485 and decided to resettle in the South of Spain, where his sister-in-law Briolanja Moniz lived with her husband Miguel Muliart (Moliaert?). While in Lisbon, he worked for the famous banking and commercial house of Centurioni, and had done so from 1476 at least until 1479, but probably until his final days in Portugal.
While under the employ of Lodisio Centurione Scotto and Paolo de Negro, he was put in charge of a trading expedition to the island of Madeira in 1476. There he was supposed to sell cloth and purchase sugar in somewhat large amounts. The commercial activity did not go as well as it should have, so his employers tried to force him to cover the economic shortcomings of the business, resulting in a lawsuit in Genoa. Apparently, Columbus never paid in full the amount he owed Lodisio and Paolo, something that must have resided deeply in his conscience, as in his deathbed he added a report on his debts, ordering 50 ducats to be paid to Paolo de Negro and Lodisio Centurione Scotto.
This is what we know for absolutely sure. However, there are literary sources, like the Life of the Admiral, written by Columbus' son Hernando. There, Hernando reports that his father had taken part in a commercial travel from Lisbon to Ireland and England in 1477, which is nothing out of the ordinary. Hernando also claims that his father sailed as far North as Thule, which would be Iceland. This is not unthinkable, but it is very noticeable detour with little to no commercial relevance. While working in Lisbon and Madeira, Columbus may have been to the Western coast of Africa, but that is just a plausible guess.
Hernando Colón, Bartolomé de las Casas, and Gonzalo Fernández de Oviedo affirm in their books that Columbus, when he was young, had sailed throughout the Mediterranean in different commercial expeditions, including one to the island of Chios. This is perfectly feasible, as Chios was an important commercial place, and it was a posession of the Republic of Genoa administered by the Giustiniani family. We can consider this claim as valid.
Things get a little blurrier now, as Hernando Colón also made some unsubstantiated claims in order to make his father look more important. In the Life of the Admiral it is said that Christopher Columbus had served as commander of the galleass Ferrandina under the banners of king René d'Anjou during the Catalan Civil War, and that while commanding that galley he sailed from Sardinia to Tunis to avoid having his ship captured. Thing is, there are no records of Columbus ever being under the employ of René.
Hernando also says that his father was travelling with a Genovese fleet in 1476 which got attacked by French pirates off the coast of Cape Saint Vincent, resulting in his ship sinking and him miraculously managing to swim ashore. This claim is quite dubious.