Finally, after a 39-day voyage, which though successful was somewhat longer than usual because of head winds, the Saints landed on the first of June at New York. From the Reminiscences and Journals of James S. Brown who had been appointed president of the saints making this journey to Zion, we learn, “And June the 8 (sic) we cast anchor in the Bay of New York having had the measles and whooping cough and 7 deaths on the passage; out of 700 souls.” 
For David and his children and Adeline there was no Statue of Liberty (not until 1885) to greet them as they stood on deck watching to catch a glimpse of this new life that awaited them. Instead they left the ship to go to Castle Garden located on an island off the southwest tip of Manhattan.
Castle Garden was the predecessor of Ellis Island. At Castle Garden, which was a remodeled fort that in 1855 became America’s first receiving station for immigrants; the immigrants were registered, were able to exchange money at a fair price, obtain train tickets, and even find a place to stay until they could continue their journey to Zion.
David and his family, and Adeline, along with many of the ship’s passengers, traveled by boat and train from New York to St. Joseph, Missouri. Margaret in retelling this experience said they travelled up the Hudson River in boats, camping on the side of the river at night, and that that they travelled through Canada to avoid the soldiers. This was the time of the Civil War and trains were often commandeered to haul soldiers and/or supplies. James Steven Brown, a passenger on the John J. Boyd travelled that same route and wrote a more detailed account of that journey in his journal: “…traveled via the Niagara Falls along the Lakes, to Detroit, and to Chicago via Quincy, Hannibal, to Saint Joseph, (Missouri) from there to Florence, Nebraska, by steamboat.” 
How long the train journey took I do not know, but it was six weeks from the time they arrived in New York until they left Florence, Nebraska on July 22, 1862, in the Homer Duncan wagon train. Part of that time would have been spent waiting for a wagon train to come from Utah and in preparing the wagons for the journey to Utah.
By1860 LDS Church leaders had abandoned the handcarts as a means of moving immigrants across the plains. This was done for two reasons: one was that even though the handcart companies were cheaper and faster than wagon trains, they were never very popular. If given a choice, the immigrants preferred a wagon train, even though the wagons were only used for supplies, and everyone except the sick, very young or very old walked the entire distance to Salt Lake City. The second reason was economics. The wagon trains left Salt Lake City loaded with flour, beans, bacon and other commodities that could be sold for cash to purchase items not available in Utah. On the return trip to Salt Lake City, the wagons were loaded with items to sell in Utah, and food and other supplies for the wagon train and the immigrant’s journey to Zion, plus a limited amount of the immigrants’ personal property. 
 Reminiscences and Journals of James Steven Brown” http://lib.byu.edu/mormonmigration/voyage
 Brown, http://lib.byu.edu/mormonmigration/voyage
 1860-68, Mormon Emigrants (Church Trains) an article on the Pioneer 1848-1868 Companies – Heritage Gateways, http://heritage.uen.org
Rigby, Helen. "A History of David Nathan Thomas and his wives, Mary, Adeline & Frances." Utah: n.p., 2011.