I don't technically go on walks, but when day hiking, I really like Merrel. For running, New Balance is my go to. Both have wide sizes and as my feet have been getting picky as I age, both can be worn comfortably for long periods without any kind of foot pain (for me).
For your walking though, I'm going to lean to New Balance. Lightweight, durable, and comfortable. If it becomes your choice, it's best to read Amazon reviews, as in the last few years the sizes of different models have varied slightly, tending smaller, so depending on the model, you might want to order a 1/2-1 size larger than normal.