I've eaten at BOG four times now. The first three times we were seated in the ballroom. Now, as amazing and as wonderful as the ballroom is, we were hoping we'd be seated in the West Wing at least once, but that didn't happen. Of course, the ballroom has a LOT more seating than the West Wing does, so your odds of being seated in the West Wing are on the low side.
As others have said, you do NOT get to pick which room you are seated in at dinner, although you can make a request--but again, given the smaller size of the West Wing, the chances are against you. Regardless, you can walk into the West Wing to look around if you end up being seated in the ballroom.
After our third dinner in the ballroom, we really wanted the chance to eat in the West Wing, so we decided to go for lunch so we'd have at least the chance of getting a seat in the other room since you can choose your own table at lunchtime. Even getting into the restaurant early for lunch the West Wing was full (ugh!). However, after noticing one table about to leave, my wife and I s-l-o-w-l-y made our way around the room, only to double-back and grab the table where people had just left from--whew! It was very atmospheric and we were thrilled to finally have had the chance to eat in the West Wing!
I'd say the only "bad" tables in BOG would be if you are seated in the ballroom in the back half farthest away from the windows with the falling snow (which is a lovely effect if you are close enough to enjoy it). If you are in the back half of the ballroom you do get a wonderful overall view of the restaurant, but you will miss out on enjoying the falling snow if you are too far away. And yes, it does take your eyes some time to adjust to see the snow if you are coming in from daylight outside.
Here's a photo of the West Wing from our table: