For research on where to apply, GoHunt and Huntinphool have been the best for me in the past.
For maps, I've used OnX and Basemap. I use only Basemap now as the subscription gives you all states for less money than OnX and the off-grid featuers on Basemap work well. And I get the hunting overlay for it as you can turn on the layer that shows GMU and harvest stats, which is nice.
Some of the states have very good research sites themselves. For example, the Utah DWR provides a very nice website for researching GMUs within Utah with harvest stats, etc. as part of the map as their "Hunt Planner".
So depends on what states you're looking at.