Hi,
For offline/local basemaps you should be using a Tile Package (.TPK), created with ArcMap or extracted from ArcGIS Server. You can also use "exploded" tile caches (i.e. a direct copy of an ArcGIS Server cache) as long as they use the compact cache format. Performance of these tile caches is usually very fast and you won't noticeably see any white space where you would expect to see tiles. You're correct that the accelerated display mode can't dramatically improve performance of tile packages, although it may be a little faster.
As you've noted, the area where the accelerated display does dramatically improve performance is with graphics (GraphicsLayers) and any layers which derive from graphics (e.g. FeatureLayers).
I would advise starting with the accelerated display enabled via the property on the Map and if you find layers or symbol types which you need to use that are not supported then consider whether there are alternative layers, or more likely, alternative symbols/renderers you can use which are supported. Typically this just means avoid creating custom symbols via ControlTemplates and stick to the esri symbol types (SimpleMarkerSymbol, PictureMarkerSymbol, etc).
Cheers
Mike