The clue and the most difficult part of the trip is to find "the correct place" so that each member of the family feels like he/she enjoyed the trip. I would expect that your 6 & 8 years old kids would prefer places such as zoo, circus, gardens and similar activities. For this purpose, I would suggest that you take a look at this link:
Bestinlebanon.com | lebanon Zoo
In this link you can also find places that fits for you and your wife such as museums and historical sites. This might be boring for small kids :-(
In the following link:
Ministry of Tourism :: Destination Lebanon you can choose "winter" from the "Four seasons" and then you can search for Nature & Adventure Attractions in different regions of Lebanon. For Christmas spirit, I would suggest that you choose the region "Mount Lebanon" and explore the different "caza". There are a lot of nice and historical places to visit. I would expect that these places are "colored" by Christmas atmosphere.
At the end I suggest that you take your family and visit "Harissa" by using a gondola lift and enjoy the trip up (ca 10 minutes) as well as the site from the top... (It is fantastic and a "must see" from my point of view).
You can read more about Harissa her:
Harissa, Lebanon - Wikipedia, the free encyclopedia
Regarding Hotels/Apartments, I have no experience with living in hotels, so I will not give any recommendation regarding prices, services, comfort etc...., but it might be a good idea to search a bit on the internet. I found this link that might be useful, you can choose hotels by region from the left side menu:
Lebanon Hotels by Map Locations - Book Hotels in Beirut Lebanon
Hopefully this will help you a bit. Good luck.