About how long is the walk from DI&S? Would it be faster to walk there with a group of 7 (including grandparents, a 7yo and toddler in stroller) or wait for the shuttle?
DI&S is literally AT the crosswalk. Along with PVI, BWPPI and Tropicana, you can't get closer. Even the Grand Californian can be a longer walk depending on where your room is. This is why so many people will stay at these places, even though they're not new and not fancy. They are so close you're at the security tents in 5 minutes. It's a snap to walk back for a rest midday, while the crowds and the heat are the worst, and head back later for parades and shows.
If all you need is a place to crash and shower, look at Google Maps along Harbor Blvd and pick whichever is cheapest. There are a few that have more recent refurbishment, better breakfasts, nicer pool areas for the kids. It all depends on what's important to you. For us, the kids aren't little any more, so the pool is not a big thing. We don't care about a lame breakfast (DI&S) because we prefer to keep a few things in the room-- most have mini fridges and microwaves- and eat a quick breakfast as we get ready, yogurt, fruit, granola etc. Just a tad bit farther down the street, Grand Legacy at the Park is getting nice reviews since they changed hands, and the pool looks nice-- thinking about trying them since they've had some really good prices. Fairfield up on the corner gets good reviews. HoJo, across the street from Fairfield, is quite nice and has an awesome water playground, nice rooms, but no breakfast. Just check out the reviews, like on Trip Advisor and here, and see what fits your needs and your budget best.
We stayed at the Grand Californian for our very first trip, and I'm glad we had that experience, but since we can get DI&S for around $100 a night usually, that's our go-to. It's not great, but it's all we need and it's SO close.
ETA: Looking at your post again, you mention Disney categorizing hotels as "Superior" Good Neighbor etc. It sounds like you are buying the package through Disney? If that's the case and you haven't pushed the button on that yet, consider NOT buying the package but pricing out everything separately, and checking what the difference in cost would be. Disneyland is quite different from WDW in that they don't do you any favors with their package pricing. You can often save quite a bit by booking airfare, transportation, hotel and tickets separately.