Just a preface, I am a former Accounting & Finance recruiter in NYC and have experience with real estate companies.
Getting a job in real estate finance is certainly a great way to start out in real estate. Since you are at a top business school, I would take advantage of their career center, events, and alumni network (reach out to alumni from your school that work at target firms) to break into the space. You can broaden your search to real estate investment firms and investment banks, as well PE - that should open some more opportunities.
Alternatively, you can look into roles with the top commercial brokerages, I know the big ones have world class training programs that will greatly increase your real estate investing knowledge. Plus you'll grow a big network if you take that route.
Feel free to PM me if you have any questions! @Zack Mattin
Bonus Tip: Don't be afraid to pick up the phone and call the alumni or ask people within your current network for introductions to people within your target firms.