looking for a compatible "menu management" plugin

What you can do is to create a fieldset with custom fields and these will be the menu for the restaurant post type. You can then set them to be displayed in the sidebar or in the detail tab, in the listing page.

First add a Fieldset, set it to be displayed in the detail page and then set it to be displayed as a tab. under it, add your fields and do the same, you’ll find the fields under the Fieldset tab.

(I assume you already have the custom post type addon)
From the next version you will be able to show the fieldset as a tab, from now you can show the PDF on the “More info” tab or in the sidebar, see steps below:

– Go to the Geodirectory settings, then click on your post type’s setting (eg. Place Settings)

– Click on the File Upload field, expand it on the right and fill it as you wish. Flag “Show on Detail page” and it will appear under the “More Info” tab…or flag “Show on sidebar” to see it on the sidebar

(the following is for when the next version will be available, so this will be your custom “menu” tab)
– Click on the Fieldset field and you will see it appearing on the right side, drag it below the File Upload field you created before, expand it and fill it as you wish, flag “Show on Detail page” and “Show as a tab on detail page”