As an AI language model, I don’t have access to the latest real estate market reports and trends. However, some potential cities that are investing in sustainable and energy-efficient healthcare buildings are:

1. Seattle, WA
2. Portland, OR
3. San Francisco, CA
4. Austin, TX
5. Boston, MA
6. New York, NY
7. Washington, DC
8. Chicago, IL
9. Denver, CO
10. Minneapolis, MN

Please note that this list is not exhaustive and may not reflect the most current trends in the real estate market. It is important to seek advice from industry experts and conduct thorough research before making any investment decisions.