EVENTS

T-Rex Trek National Tour

To celebrate the DVD release in 2007, a model of Rexy made a tour across the contiguous United States. It began on 17 April, and the DVD released on 24 April.
Images of the sendoff available on Getty Images.

Rexy at the San Diego Zoo

To promote BotS, an animatronic Rexy was put on display near the gift shop of the SD Zoo.

Kahmunrah's Loot Pile

From May 4 to October 1 2009, the pile of loot Kahmunrah gathers was present in the Smithsonian to promote the film. The pile was composed of replicas of actual Smithonian exhibits that were present in the film, including Archie Bunker's chair and the ruby slippers.
The exhibition, archived on the Smithsonian's website.
A picture of the exhibition taken on 1 July 2009 by Christina B. Castro.

South Bay Drive-In Giveaway

A sweepstakes held by the South Bay Drive-In Theater. The winner was "Sacajawea P.", likely a pseudonym.

Secret of the Tomb

Gala Screening
A pre-release screening for reviewers and film critics.
Content warning: One of the images on the source site has a non-Native American dressed in Native American regalia. Viewer discretion advised.
Source: KidzCoolIt

Union Square Character Meet-Up
For a week before the film's release, a group of performers played in character in Union Square. Teddy was played by Ray Reinson, Lancelot was played by Paris Black, and Octavius was played by Jagger S. Gordon. Attila's performer is unknown. Photo album courtesy of Ray Reinson. [IA Backup, did not save images]

Regent Street Holiday Lights
Regent Street is a road in London, one of the first purpose-built shopping streets in the city. It's been the filming location of many a scene, and it's also a place known for film promos. With the premiere of NatM 3, the street was lit up with string lights and characters from the films walked around; available to take pictures with.
Source: KidzCoolIt

These events are not officially licensed. It's essentially a dumping ground for local events that use the literal phrase "night at the museum" and some vague imagery (mostly T. rex skeletons and monkeys). You'll also find more of these on the Bootleg page, which is where we put the more soulless events like fundraisers and MLMs.

Museum Sleepovers

Body Worlds: London, 2009. Via the O2 Cinema. [Source]