I'd suggest that the map show the land areas as rectangles (and circles) next to one another, but include a 3D picture of the cylinder to help give the scale. If your skills are more in drawing flat maps, you needn't feel intimidated by trying to draw a 3D perspective view and keeping it current as your maps progress. That's the easiest part for a 3D modeler. I suspect there are people here who'd be glad to help project your maps into a model.

Don't forget that the interior surfaces are only part of it. There are multiple levels "underground" as well as in and on the end caps.