Spain never did such a thing, but we need to get into the matter of how or why did Spain not venture that far North in North American territory, which requires a quick point on the logistics. So, as good old Jack said, let's go piece by piece:

the east coast is a straight shot from Spain

This point is geographically correct, but logistically incorrect. Spain is indeed in the same latitude as the former territory of the American 13 colonies, but the maritime currents make it unfeasible to travel straight from Spain to New York, as you would be going against the Gulf Stream, and quite against the winds. Here you have a map showing the most important currents in the North Atlantic.

Spain's ordinary route for going to the Americas was through the Canary Islands. Ships would normally sail from Andalusia: Palos, as in Columbus' first voyage; or Cádiz, in Columbus' second voyage would be the ideal starting points, as proven by the many expeditions that departed from there. Vicente Pinzón, Alonso de Ojeda, Juan de la Cosa, Amerigo Vespucci, Alonso Vélez de Mendoza, Diego de Lepe, Rodrigo de Bastidas, etc sailed from the Atlantic coast of Andalusia, and from then went to the Canary islands. From these islands, you can profit from the Canaries' Current, that would guide you to the Leeward isles or to the coast of Brazil (vide Pinzón's discovery of Brazil, Columbus' second journey, or Diego de Lepe's expedition of the year 1500).

This, and Columbus' first two journeys lead to Castile establishing settlements in Hispaniola and Cuba, for they were the most convenient islands for travelling, and they still were in the late XVIII century when the Count of Aranda proposed a plan to divide the Spanish America into three kingdoms, leaving Cuba, Puerto Rico, and Santo Domingo as possessions of the Spanish Crown that would act as advanced commercial points and in some measure as freeports. Cuba, Havana in particular, was the last stop of the Treasure Fleet before sailing into the high seas en route to Spain. Check the above attached map to see the route.

With the government established in Santo Domingo, and having a captain-generalcy in Cuba, the Spaniards could venture into the conquest of the continent. Cortés and his men set sail from Cuba, arrived in Mexico, and the rest is a very long digression. Mexico, being heavily urbanised, became a capital city, and it could not have happened otherwise. Soon, Mexico displaced any other city in the Spanish America and became a metropolis of its very own, with the viceroys managing the ordinary stuff as if they were kings. This meant that expeditions for discovery and conquest of new territories would depend on the viceroys and the Real Audiencia (the Court of Justice). Expeditions like the ones lead by Hernando de Soto, Alvar Núñez Cabeza de Vaca, Oñate, and others depended on Mexico, and to a lesser degree on Cuba.

Now come to think of how immensely far away the land of the 13 colonies id from Mexico, and how logistically difficult would it be for the viceroy of Mexico to send people there, let alone administer those territories. Spain simply never had the logistics or manpower to venture into those Northern lands. So, back to the original question: Spain nevery gave that territory, for it was never under any sort of Spanish control