For actually running (as opposed to just casual use), Nike was never actually my first choice. I used Brooks in the past, and recently Hoka - both of which I think are great shoes. Unfortunately both are US based.

For a non-US company, maybe give Asics (Japanese brand) a look? They never really fit me right personally, but I know they are popular amongst runners.

And just to clarify - I don't think any of the brands above sell proper "wide toe box" shoes that I mentioned above. Xero and Altra are the best known brands (both US-based) in this category I think. There are also some really inexpensive options from Chinese companies on Amazon that I think are actually worth a look - Whitin seems to be the most popular on Amazon in the US, but I see the same shoes sold under different brand names. These shoes tend to be really light weight and comfortable for casual use or working out, but they just don't have enough cushion where I would want to run long distances in them.

Oh and Skechers sells some wide toe shoes as well - not as roomy in the toe box as the brands above, but still super comfy. But again, not something I would recommend for running.