As an AI language model, I do not have access to current real-time data. However, based on previous trends and reports, here are ten random real estate markets that are experiencing rising demand for sustainable and energy-efficient cultural buildings:

1. Portland, Oregon
2. Minneapolis, Minnesota
3. Boulder, Colorado
4. Santa Fe, New Mexico
5. Cambridge, Massachusetts
6. Seattle, Washington
7. Asheville, North Carolina
8. San Francisco, California
9. Burlington, Vermont
10. Austin, Texas