Per item, without touching the source data. Open the Menu post under Steuard → Menus, select its Overrides tab, click Edit overrides…, expand the item, and turn off Price. The change applies everywhere that Menu post is displayed — block, shortcode, and classic placements alike.
This works for flat prices and multi-size price lists alike — the item and its description stay on the menu, only the price disappears. Each section also offers Hide all / Show all controls for one-click bulk changes.
To hide every price instead, turn off Show prices on the Menu post's Display tab. To suppress only $0 prices, set Items priced at $0.00 to Keep the item, hide the price — see Menu Prices, Sizes, and Currency.
See Creating a Menu for the rest of the Overrides editor.