Can you create a drop down menu after a check box or radio button is selected?

You can use Condition logic feature to show/hide field base on rules.

User guide: Smart-Forms-Using-Conditional-Logic

Here is a test form https://form.jotform.com/61438868326971

OR 

If what you were looking for is a comprehensive Order menu, you can check this thread for similar solution

https://www.jotform.com/answers/711954-How-to-have-Order-Menu-using-Form

demo form : https://form.jotform.com/53286246358968?

Let us know if you need further assistance.