We are in the planning stages of doing an across the US - West 2 East ride to raise money for polio for the Rotary. Being new to riding we want to avoid hills :-)One of the three Adventure Cycling routes is what I would recommend. The Trans America is great. The climbs in the west are long but not very steep. My two companions had almost no miles under their belts and just started off with shorter days in the first couple weeks. They did fine.
The Northern Tier is supposed to be nice too. The Southern tier is shorter and flatter, but you don't want to do it in the Summer.
The hard climbs are the short steep ones in the east and if you are going W - E you will be in shape by the time you get to them, Just be sure to pack light and have low gears.