The two resorts that my family usually waffles between are the Grand Floridian and the Beach Club.
At the GF, you are one easy stop away from the Magic Kingdom. This is insanely convenient, especially if you are still dealing with a stroller. The hotel is gorgeous with spacious rooms and top-notch service. I love listening to the live music in the lobby in the evenings and exploring the many shops. You also have here the benefit of many dining options on-site. There are counter service, table service, and signature dining options all right at the hotel. Despite the outwardly refined atmosphere, there is nothing stuffy about the GF.
At the Beach Club, you are a five minute walk away from Epcot, a seven minute walk away from the Boardwalk recreation area, and a quick boat ride away from Disney's Hollywood Studios. You also have large rooms and great service here. If you consider the nearby options at the Yacht Club, Swan & Dolphin, Boardwalk, and Epcot, you're really in dining paradise. And the best part about the Beach Club is the pool. The Yacht & Beach Club pool, Stormalong Bay, is universally considered to be the best at WDW. It is really a mini-water park with a sandy-bottom area, a lazy river area, and two water slides.
During our last big family trip to WDW, we stayed at the Beach Club. We took the bus to the Magic Kingdom in the morning. Around lunch time we would come back to the hotel and spend the afternoon at the pool. For dinner, we ate in the World Showcase at Epcot almost every night. During our next big family trip to WDW (Thanksgiving!), we will be staying at the Grand Floridian. We'll take advantage of the great recreation opportunities at the Magic Kingdom area resorts and stay out to watches Wishes in the evening.
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Happy planning!