Yes, I do live in the area. Rapid City to be exact. The Mick is easily doable on a CX bike. As a matter of fact, every fall, we (the group I ride with) ride the whole thing in one day, turning it into kind of rolling party. Think of it as a gravel grinder meets RAGBRAI. Fun stuff.
How far do you want to go? If you're up for 70'ish miles in a day and you're wanting to take in the sights, I'd start in Deadwood and ride to Custer, stopping along the way at Rochford (a TINY little town in the Black Hills) at the Moonshine Gulch for a beer and/or food, then at Hill City for more opportunities to "fuel" up. Then on to Crazy Horse Monument and finally into Custer. Beyond Custer it gets fairly arid and can be miserably hot, esp. in the summer.
When are you thinking of doing it? Let me know and maybe I can help you arrange shuttling and/or ride with you as a "tour guide" if you'd like!