AKL is actually pretty remote and that's what makes it our least favorite to stay at.
As an AKL owner, AKL is really only "remote" to the Magic Kingdom - about 18 minutes by bus (same as SSR). I'd note that from the Polyneisan to the MK it's 15 minutes; it's just you're on the Monorail instead of a bus!
AKL is only 2 minutes to the Animal Kingdom. It's faster to Hollywood Studios than SSR is (12 minutes AKL vs 16 minutes SSR), and the same travel time as SSR to Epcot (12 minutes).
SSR does allow for walking to Downtown Studios, but if you're not staying at the first bus stop, there's also extra time added on for where you are in SSR - it's very big. (Add about 4 minutes for Kidani at the AKL, though, as the bust picks up first at Kidani and then stops at Jambo).
AKL has amazing theming, food, and of course, the animals. While I do wish it had more than just the bus, or a nice walking trail to the Animal Kingdom, the distance to Epcot or Hollywood Studios isn't all that far.
Obviously choose what resort is best for you and your family, but I often hear people talk about how remote AKL is, I just feel the need to jump in to correct it. Having stayed at nearly every resort, I'd personally give SSR and OKW that label before AKL. Admittedly, though, ever since the Adventurer's Club went away, I don't prioritize DS closeness as much as I used to. ;-)
You only mentioned MK and Epcot as parks. Are they your favorite and the only ones you plan to go to? If so, and if buses are a no, then you're going to want to be on a monorail resort. Otherwise, no matter where you select, you are going to be subject to buses for at least some of the park transporation.