I think Luang Prabang is already fully booked, you may get some rooms in the upper segment. Vientiane offers you some places with Christmas and New Years Even dinners. Kop Chai Deu offers a New Years Party with buffet, Ansara has a 8 course dinner, Lao Plaza and Novotel as well.

For sightseeing Luang Prabang is more interesting, since you can do some nice day excursions like the Elephant camp. Vientiane has the Wats, That Luang, maybe one museum to offer. But you can take a nice rest here, sitting at the new Chao Anouvong park at the river side (with modern and safe children playground), having a trip to the Buddha Park (good food there as well). If you are renting bicycles you can do some nice trips arround town. Go shopping at the Thalat Sao and have a coffee downstairs an Sinouk Coffee (organic Lao coffee). In the late afternoon, go to Patu Xai and watch the locals doing exercise (or join them) and enjoy the cool breeze and nice atmosphere (and the local music from the loudspeakers, but fortunatly it's not too loud).

in the evening I recommend to have dinner either at Lao Garden, a noce place o the river side with live music and Lao and international food, or try crickets and other food at Kop chai Deu (you may think it is a tourist trap, but it is not. Sit upstairs, you will see that many Lao people are guests as well. The food is good (try Luang Prabang sausage), sometimes service is a bit slow).

For day excursions just go to Diethelm Travel an Nam Phou square, they can book you all you need Pakse might be nice, it just takes some time to go there. You can visit Coffee plantations there.