We were in that area two years ago. Stayed at
http://www.spruceparkrv.com/
It was a central location for GNP, Flathead lake and Whitefish lake. Kayaked both lakes, toured GNP twice.
We didn't stay at the RV park with the intentions of doing all 3 side trips. It was mostly for GNP. We stumbled onto the other lakes. Worked out great for us.
With that being said you could still do all that staying at Flathead if that is something you're interested in.