This is not an extensive list but simply a few common sense things to do after you have a new website.
Link Social Media Accounts
If you have a website for your business you probably have setup accounts on Facebook, Instagram, and maybe Twitter. Wherever you have an online presence related to your business, link to your website. The reason is so that the search engines know the relationship between your page/account and website and also so that your customers can easily find your website.
Link Google Maps and Yelp
Listing your business on Google Maps and Yelp is especially important for local businesses because that is the audience they serve, local visitors. There are other map and local business listing services out there but if you are listed on Google Maps and Yelp that will take care of 75% of the coverage. Apple Maps uses Yelp business listings.