The majority of Monroy who traveled to America come from the region of Spain named Extremadura but also from others regions of Spain.
On reaching the New World they were distributed throughout the continent. Mostly in Chile and Mexico, but is possible to found them throughout the Americas. This a non common surname, but we can find it in almost every region of America including the United States
There were many Monroy whose ventured into a travel New Spain, including others in the Philippines and other lands conquered by the Spanish Crown.
There are those who were famous or keys in the conquest of a region.
Pedro de Valdivia, conqueror of Chile, was accompanied by Alonso de Monroy in his adventure.
Francisco Pizarro, conqueror of the Inca Empire (Peru) was joined by Diego de Monroy.
Don Pedro de Alvarado, conqueror of Guatemala was accompanied by Juan de Monroy.
Hernan Cortes Pizarro de Monroy, conqueror of Mexico was second cousin of Francisco Pizarro
One of the first actions of Hernan Cortes in Mexico after the conquest of Tenochtitlan in 1521 was the conquest of the Panuco - Tula River area.
There are those who were not famous but also sailed for New Spain (Mexico), Cartagena (Colombia), New Granada (Panama - Colombia), Gneral Captaincy of Chile Captaincy General of Guatemala, Viceroyalty of Peru (Peru, Ecuador , Bolivia, Viceroyalty of the Rio de la Plata (Argentina, Uruguay), or the Caribbean islands, as were:
Cristobal de Monroy son of Alonso Triguero, resident of Toro (Castilla) and his wife Catherine de Monroy, to the island Spaniard (Dominican Republic) on November 19, 1511 and another trip themselves on July 18, 1512.
Pedro de Monroy, son of Peter and Eleanor Guiral Monroy, resident of Toro (Castilla) on July 16, 1527.
Pedro de Monroy, the son of Juan de Monroy and Catalina de Villalobos, a native of Zamora in Cartagena Navy June 13, 1535.
Dionisio de Monroy Monroy son of Martin and Martha Sanchez, a native of the nava de Medina del Campo, on September 14, 1534.
Diego Diego Grades Grades son and Sancha de Monroy, resident of Seville to Santo Domingo with his wife Beatrice Salazar on January 28, 1539.
Son of Pedro Antonio de Monroy Pantoja and Leonora de Calatayud, resident of Avila on February 26, 1540.
Gutierrez Monroy son of Don Alonzo Enriquez de Sotomayor and of Juana de Guzman, neighbors of Plasencia September 5, 1547.
The lawyer Don Pedro Puertocarrero citizen of Seville, to New Spain as Magistrate of his royal audience. He carries his servants Anton de Monroy, the son of Diego de Monroy and Catalina Gonzalez, Bartolome de Salamanca neighbor Muñiz Santiago Muñiz's son and Anotnio dle Paso, Mexia resident of Jerez Francisco near Badajoz and son of Catherine Rodrigo Alvarez Mexia and Cristobal de Soria of Trujillo's son Juan de Soria and Constance Perez.
Gutierrez Monroy, citizen and native of Requena, son of Pedro and Juana Monroy Valencia, single, to Peru.
Juan de Monroy citizen and native of Seville, son of Alonso de Monroy and of Doña Beatriz Venegas single to Peru by Diego Montesino factor.
Pedro de Monroy son of Alvaro de Monroy and Maria Sarmiento, residents of Salamanca, New Spain, on September 7, 1536.
Juan de Pineda son of Pedro de Pineda and of Mera de Monroy, a native of Seville to Cartagena, on March 8, 1536.
Garcia Monroy, Monroy son of Peter and Elizabeth Harris, a resident of San Martin de Valdeiglesias to New Spain, May 9, 1536.
Fernando de Monroy, the son of Gonzalo de Monroy and of Juana Diaz, a native of Miradilla to the New Spain at September 17, 1536.
Alonso de Monroy son of Cristobal de Monroy and of Grade Cosntanza Gomez, residents of Salamanca to Peru on May 24, 1537.
Gabriel Monroy son of Francis of Monroy and Dona Mencia de Linares, a native of Trujillo for New Spain on April 30, 1537.
Diego Monroy Diego Monroy's son and Doña Isabel, Almendral's neighbors in Florida on March 6, 1538.
Lope de Tordoya son of Diego de Monroy and of Doña Isabel, neighbors of the Almendral, brother Diego to Florida on March 6, 1538.
Juan de Pineda son of Peter and Joanna Pineda Monroy, resident of Seville to Nombre de Dios (Panama) on April 2, 1538.
Hernando de Monroy son of Pedro de León and Isabel Monroy, resident of Zamora to Santo Domingo, August 30, 1538.
Source: Catalog of Passengers to the Indies during the sixteenth, seventeenth and eighteenth Cristobal Bermudez Plata.
Contents: v. 1. 1509-1534 - v. 2. 1535-1538 - see 3. 1539-1559 - v. 4. 1560-1566 - v. 5. 1567-1577 - v. 6. 1578-1585 - v. 7. 1586-1599.
Volume 1,2 and 3 (microfilm) reviewed by Jose Luis Montoya Monroy on 4 August 2007, at a Family History Library of The Church of Jesus Christ of Latter-day Saints.
Further information on the Family Search site
Likewise there are other sites where you interact with old documents scanned (image), indexed and stored with keyword so you can search the surnames you're looking for.
For example the Spanish government site http://pares.mcu.es/ParesBusquedas/servlets/Control_servlet?accion=0