I thought of something else...do not throw any scraps away when leveling...I keep a bowl to put all the scraps in...never know when you need to repair and if you still have cake leftover, freeze the pieces for cake balls, etc. I have a repair kit that I take with me (I include pieces of cake in a zip lock bag) when delivering my cakes.
In the repair kit, I take several Viva towels, my high density roller, the matching mediums (buttercream/fondant/royal icing). Included, also, are a clean tea towel and a spray bottle of clean water to clean my hands after it is all over, fresh gloves, the proper decorating tips, my different sized angled spatulas, tweezers, my cake lifter, a garbage bag, a little mixing bowl with a lid, parchment paper, roll of paper towels, a tray (to place everything on while repairing), my business cards, a knife and cake server (in case someone forgot their utensils to cut the cake), first aid kit (basically, a few band aids), and a bottled water (for me to drink after I have it all 'perfect'). Always take extra pieces of decorations (like filigree, gum paste flowers, ribbon, etc.). You never know what will and can happen on your way to the venue
I know I am forgetting a few things...oh, yes, my cell phone...what else?