It is easy to locate a place or get directions using one of the major mapping sites. But to view maps showing only certain features, for example, major cities and rivers for a country, then try these sites:
Visit the Perry-Castañeda Library Map Collection for an extensive collection of country/territory and regional maps. The World Factbook is a rich source of geographic information with country/territory/region maps. ArcGIS Map Viewer has many different types of maps including topographic and ocean maps.
View country/region maps like browsing a world atlas:
If you have trouble searching for a place that comes up with no results, then try one of these sites. GeoNames has a database of 11 million places. Other sites include the GEOnet Names Server, a database of foreign names, and the Geographic Names Information System (GNIS) for U.S. places.
OpenStreetMap Compass has a compass on a map where rotating the compass will calculate the bearing, including magnetic declination. CalTopo also has a feature to determine bearing and magnetic declination.
CalTopo has a feature where the mouse cursor (crosshair cursor for the phone/tablet) displays the elevation. For GPS Visualizer, right-click on the map to display the elevation. The Free Map Tools Elevation Finder displays the elevation when clicking on a place on the map.
For a large collection of old maps, visit the David Rumsey Map Collection.