OSMAND can show both cycle routes and campsites. I've used it successfully for two European tours and have been very happy with it, getting to know the user interface can be difficult.
To show cycle routes: with the map showing, press the bottom left menu button and choose Configure screen
scroll down to the bottom and tick the box labelled Show cycle routes
They appear at zoom levels 12 and up, equivalent to the 2 mile scale. (You can briefly see the zoom level above the zoom buttons bottom right when you change scale, though it gets replaced by the scale.)
Campsites are one of many types of POI that OSMAND can display and the assumption is that you don't want them all there all the time, to minimise clutter. To display them: Long press on the screen in the area you want to see them and tap the location box that appears; Choose Search near here
; Choose Accommodation
; Tap the 'show on map icon' (bottom left of the screen)
This will show campsites and other forms of accommodation, each with their own icon, at zoom levels 10 and up.
To just get campsites, tap the filter icon below the search list and type 'camp' in the filter box at the top. Show on map will then just show campsites, and as far is I know there's no reason why you shouldn't just leave them there all the time (but I haven't used it like this).
There are so many other useful POIs that my touring routine is something like this:
scroll ahead to the area I think I'll reach and use 'search near here' to find possible campsites;
choose one and set it as a favourite, which can be displayed when others have been hidden;
use 'directions to' to plot a route to the campsite (which I didn't necessarily follow, but they were usually pretty good);
use 'search near here' somewhere along the route to find a supermarket to buy food.
There are loads of other useful POIs which you probably wouldn't want on all the time, but can be really useful, such as cash machines, pharmacies, tourist information, etc. I think the range of information stored in offline OSMAND is phenomenal, and it's worth a bit of effort getting to know how to use it.
I also have a Garmin etrex in which I have maps from http://garmin.openstreetmap.nl/
I've found these to be pretty good. I think it has all the same POIs as OSMAND. I don't trust its routing, it's lead me on odd detours too many times. I generally find OSMAND easier, so I use that for planning, and then have the Garmin on the bars ready to show detail along the way when needed.