What LocalBusiness markup does
It tells Google, in a format it can't misread, your business's name, type, address, phone number, opening hours and location. Google requires the name and address and recommends the rest.
Pick the most specific business type that fits (Dentist rather than LocalBusiness, for example). It helps Google understand what you do.
Markup plus Google Business Profile
For the map results and the local pack, your Google Business Profile matters most. Keep the name, address and phone on your website and in the markup exactly the same as on your profile, so Google can connect them.
Where to put it
Add the code to your homepage, or to the page for each location if you have several. Each location gets its own block with its own address and hours.