I have and use the Avenza app and it works well. It does require that the map you download be a geo-rectified PDF file but as mentioned it will show you where you are and is not dependent on having cell phone coverage.
Another app I use is US Topo Maps which allows you to choose what type layer (topo map, aerial view, road, etc) is displayed. It also has a bread crumb tracking feature which will display and save your track log. Pretty sure that you need to open this app up and get current location before you get out of cell coverage.