Below are some hotels near Te Papa, in the CBD. Please contact them directly to book your accommodation.
QT Museum Wellington Apartments
90 Cable St,
Te Aro,
Wellington 6011
Copthorne Hotel
100 Oriental Parade, Oriental Bay, Wellington 6011
https://www.millenniumhotels.com/en/wellington/copthorne-hotel-wellington-oriental-bay/
Transport
Suggested taxi companies:
Green Cabs Wellington:
0800 464 7336
Wellington Combined Taxis:
04 384 4444