I really like the idea behind this design and it's a good starting point. I would recommend tweaking the design so that its more of a lockup that can easily be recognisable across a variety of different outputs (print and digital) Have a try at using different fonts that will help give it that Chicago pizzeria feel. An icon element can always be optional in a logo design and don't feel that you need to have one. If you'd like to have one in your design consider other elements that relate to a pizzeria ie roller, woodier pizza oven, pizza box, pizza cutter, pizza chef etc.