I have played Franklin Hills (I worked there in high school just to be able to play the course on Mondays) and I have played both DGC courses, North and South. I walked Inverness in two US Opens; I stood next to Lon Hinkle and watched him hit driver AROUND the Hinkle Tree the morning after the USGA planted it.
Franklin Hills - A real, rare treat. Tom Doak spoke highly of it in The Confidential Guide, and all of the massive improvements actually were completed AFTER Tom's praise for it. My guess is that Tom would like it even more now, and would be an enthusiastic supporter of the faithful restoration work that was done there. I do think that if Ross were here today, Franklin is the one he'd be most pleased to see. His routing fits the land so well, and so little has needed changing.
DGC - That club has a ton of very good players, and they have placed so many demands on the North Course (the big course at DGC) that it is now slightly unrecognizable from what was originally there. I have never been a big fan of the North Course; it is built on flat land and unlike, say, Garden City or the recently-featured Brookside in Columbus, it appears to be a course that is uncomfortable with its flatness. The North Course always felt two-dimensional to me.
But the DGC South Course, a Par 68, is a beauty. Built on the same flat land, but having escaped the attentions of the tournament committee, it has a different appearance to me. Full of Ross's character in the green complexes. I love the little South Course.
Inverness was always a shock to me in how small the greens appeared when you had to hit into them. It always seemed to me a course that built tension in where you placed every shot. That, I suppose, is a mark of a good course. It is a beautiful layout that could probably stand just a bit of the Oakmont tree-removal program. I thought I was going to get a chance to play it for the first time last August after having walked it twice, but my host had to defer until next season.
All three clubs are really special places; what a fortunate invitation for you.