Wrap around Cylinder

create text/art you wish to wrap

make a symbol of the text/art (drag into symbols)

draw a circle of the diameter you want to wrap around

with the circle selected, go to Effect → 3D → Extrude & Bevel

select position: top, and set an extrude depth as tall as you need the cylinder to be

click the Map Art button

select the outer surface of the cylindar (cycle until you get it right)

pick the symbol you made of the artwork

position the art accordingly