A co-worker (fellow DISer and friend too) and I just helped another co-worker and friend with this same decision. Our friend was booking only about 2 weeks in advance, and had a really high budget (compared to our usual budgets) and we suggested BC which she and her family LOVED. They were bringing their 2 older children, who are 5 and 3, and they loved their trip.
My own opinions are similar to PPs. I've always wanted to stay at the Poly, but since we own DVC we tend to stay at DVC resorts now. I agree that the long houses can be very far from the "action" though, which is another reason why we haven't stayed here (besides cost) however we do spend a lot of time here, just enjoying the restaurants and buzz around the resort.
I would never stay at CR because I think it's way over rated and boring. We did check out the BLT area last trip, which seemed cool, but I'd rather use my DVC points at OKW. I do love the stores at CR though!
WL is super special to me! It was my first onsite resort, and it's where we were staying when we got engaged. I love the theming and the CMs always seem friendliest IMO! I love hopping on the boat for the ride to MK! I love the pool area; I love whispering canyon cafe too- what would a kid want more than all you can drink milkshakes!
AKL is a great resort too! My biggest complaint is the location- it's so far away from everything (except AK!). The pool is awesome, the restaurants are interesting, and the Mara has really awesome pumpkin soup! Like WL, the rooms can be far from the action, but at least you're still connected to the main building, as opposed to the Poly.
We always rent a car, and we try to avoid the buses as much as possible, but that's just us. If you have a car, where you stay doesn't really matter as far as getting around places; you don't have to worry about your kids being unrestrained in a bus that's going fast, and most importantly, you always have a seat!
I wouldn't discount the Epcot resorts- great locations as far as getting to Epcot and the studios. SAB might be too exciting for your little ones, but the pool at BWI is cool too, and the theming at all Epcot resorts are great! Beaches & Cream has the best burgers on property IMO!