If motel-style lodging is out AND you want a true suite AND you want something within walking distance, your options are pretty limited. You can have two of the three with no problem, but all three are few and far between.
All three Disney hotels will have one-bedroom suites. I honestly don't hear many people complain about the Paradise Pier, and most people actually rave about the theme-park view rooms. The grounds and pool area aren't anywhere close to as impressive as the other two on-site properties, but they are certainly adequate and a step above most of the walking-distance off-site hotels.
In terms of off-site hotels, the Hojo is probably your best choice. It has kids suites, but they have bunk beds in the kids room, which might not be ideal with the ages of your kiddos. It also has a water play area, that would be a huge hit with kids, as well as a "normal" pool. I think it's your best option off-property in terms of the criteria you've set out. It is the most "resort like" of the bunch, and has interior hallways.
Pretty much everything else on Harbor has motel-style exterior doors. Many have some very nice suite options, but are not anything close to "resort style." They're clean. They're close (many are even closer than the
Disneyland Hotel and Paradise Pier). They have suites. But no one would mistake them for a resort hotel.
I think the Desert Palms has indoor hallways and suites. I wouldn't call it "resort style" in the least, but it does have a pool and I think breakfast. Never stayed there before, and it's at the limit of what I would consider walking distance.
The Anabella has some great suite options, but it's motel-style. Honestly, though, the grounds are lovely, the pool is decent, and I've had two great stays there. Definitely walking distance if you cut through the lobby of the Grand Californian and out into Downtown Disney.
The Residence Inn is also not what I would call easy walking distance, but many people do walk. Lots of suite options, but exterior doors. Right on the ART transit if you don't want to walk.
In all honestly, those are the only options that I would say meet the criteria you specified. There just aren't many "resort style" options around the parks (It's a major difference from WDW for sure). Clean, comfortable accommodations abound, but they're just not "resorts" in the traditional sense of the word.