ArcView 10.1 does not have this kind of topo map to "Add Data". Where do I find this type of topo map, preferably free. ArcGIS online does not seem to offer this type of topo, unless I am not seeing it on my side.
It may not show up under the Basemap dialog, but Esri does host a US Topo map service. The service uses scale dependent rendering with 4 levels, a colorized shaded relief, 250k topographic, 100k topographic, and 24k topographic.
ArcGIS Server REST endpoint