What are good techniques for photographing art and interiors in a museum without flash?

First thing first: check the museum photography policy. It's usually available on the museum Website. Ususally, photography is permitted in the permanent collections but not in the temp exhibits.

From the MET Website http://www.metmuseum.org/visit/tips/

Photography

Still photography is permitted for private, noncommercial use only in the Museum's galleries devoted to the permanent collection. Photographs cannot be published, sold, reproduced, transferred, distributed, or otherwise commercially exploited in any manner whatsoever. Photography is not permitted in special exhibitions or areas designated as "No Photography"; works of art on loan from private collections or other institutions may not be photographed. The use of flash is prohibited at all times and in all galleries. Movie and video cameras are prohibited. Tripods are allowed Wednesday through Friday, and only with a permit issued by the Information Desk in the Great Hall.

For press and other special photography, including film and videotape projects, please contact the Communications Department during business hours by phone (212-879-5500, ext. 3441) or fax (212-472-2764). See The Image Library for more information about requests regarding photographs of works of art owned by the Museum for any purpose other than private and noncommercial.

The Museum reserves the right, at its sole discretion, to withhold and/or withdraw permission to photograph on its premises or to reproduce photographs of objects in its collection.