I LOVE Sauze - have been 3 times - once with friends, once with the same friends and kids (theirs, not ours) and once as a couple. We've always stayed at the bottom of the Clotes lift (once in the Hermitage, 2x in Stella Alpina - would go back to the latter in a shot). There is one noisy-ish bar near there, but it's never bothered us at all. The noisier bars are all further down the hill in the centre. I've read loads about it being a 'party' resort, but wouldn't have put it in that category based on our visits (10 years between first and last).
It's much better to be near Clotes than down in town - saves the walk up the hill! If you're not beginners, you can just get straight onto the lift and you're away. If you've got beginners in your group, you'll need to get the Sportinia lift, which (realistically with kids) is a trip on the ski bus, but it's a very efficient bus so that's not a bother.
Wind can be an issue, but there's plenty of skiing in Sauze itself - it's mainly the link to the rest of the Via Lattea (and Sestriere) that gets closed. We were over in Sestriere last year when the wind started to get up, so we had to get the lift back up to the top and ski down into Sauze in some pretty 'interesting' conditions, but it was all very well controlled and orderly (ie - they weren't letting you get on the lifts unless you needed to be in the other resort).
The point made upthread about the lifts being slow is definitely true. BUT - on the plus side, the queues are short. We spent much longer between runs in Alpe d'Huez, when the lifts were fast but the queues were endless.
I think it's a lovely resort, with a great ski area. The mountain restaurants and cafes are lovely (and a fraction the price of those in France), the transfer is short and the views are great. I'm pretty sure we'll go back again in the next couple of years (we would have gone there this year - with a family - but for the fact it's not really suitable for one of our party who is a very nervous beginner).
Only thing I'd say is that if your cheap deal is for the Hotel Hermitage, it's not a great hotel. We were there 2 years ago, and it was pretty run down, very basic food indeed and a bar/lounge where you didn't really want to spend any time. The rooms were basic to say the least. It was 'OK' for the price, but I'd rather have spent a bit more and had a much nicer experience.
If your deal is for Stella Alpina on the other hand, can't recommend it highly enough! Lovely rooms, friendly staff and very tasty food. And a homely lounge/bar which is very family friendly, and a lovely place to spend the evening.
Are you looking at this season? Snow has been amazing - check out sauzeonline.com - he does a snow report every friday which will give you a great feel for what it's like on the slopes.