Well the answer is going to be a theory, and not fact, because no person can say exactly who would have discovered America. But at the time of Columbus, Spain and Italy were the main countries sending our explorers, so most likely it still would have been an explorer from that region. Also it could have been France or England to since there were many explorers coming from those countries.
If Columbus had failed to failed to reach America in 1492, it is quite likely that other explorers from western countries like Spain and Portugal would have again tried to find a sea route to India by sailing West and found America.
At that time there was great interest among explorers to find a sea route to India. Also the concept of a world that was spherical rather than flat, was also gaining ground among many enlightened people of that time.
It is all a matter of guesswork - we cannot be sure of anything in mattrers like these - but I see no reason why, Vasco de Gama, who found a route to India going around the the Cape of Good Hope, would not have tried the Western route, if Columbus had not found America blocking that route.
However once the sea route to India round the Cape of Good Hope was found out, the chances of people trying to find out another route through West would have definitely reduced. Still I believe that other explores would have definitely tried to explore the spherical world further and found out America before end of sixteenth century.
It is interesting to note that Vikings had reached the American continent much before Columbus. A Viking, Leif Ericson established a base on a part of North America in year 1000, which is now a part of Canadian Province of Newfoundland. Vikings abandoned this post in 1014.
It is possible, if Columbus had failed that it would have been assumed his ships fell of the edge of the earth and all exploration would have stopped beyond the coastal hopping the Portugese were doing along the coast of Africa, so if a European nation was to be created with deiscovering the New World without a successful Columbus voyage I belief the Portuugese would have, going the long way around Africa and on to China