Most consumer brands hire graphic designers to work on internal correspondence as well as external customer-facing projects.
Build a portfolio to show the work you've already completed and other work you intend on finishing you will be able to get feedback from these groups or classmates. Their direction can shape your work and make solid first impressions.
Tech companies. Come to the Bay Area if you're willing to relocate. This is one of the biggest hubs for graphic designers. Small mom and pop branding agencies tend to be a bit different than the bigger ad agencies. The smaller branding places allow you to be a true artist while not getting lost in the politics of ad agencies. Hope this helps! (p.s. I've heard that freelancing is more lucrative than full-time employment with a company)
Many/most decent-sized brands have in house designers. B2B companies, tech companies, local/small businesses–print shops, marketing companies, strategic messaging companies–the list goes on. Agencies are an obvious answer, but if you go to linkedin and look at who's hiring designers, you'll get an understanding of the wide scope of businesses that hire designers.
I've worked for both–agencies and as an in house designer (as well as been a freelancer for over a decade)–there are MANY opportunities for designers.
Troy recommends the following next steps: