The truth is, I've just been using Eagle to open Arduino's board design files. I'm using Eagle 7.7.0, which is the last one that doesn't require the online account. I know that some of Arduino's design files are not compatible with the latest Eagle versions (though it's easy to fix them), so you might be best off using Eagle 7 anyway.
I generally prefer Kicad, and I know the support for Eagle projects has been improving over time, but I haven't checked how the latest Kicad does with these files. Have you given Kicad a try?
I haven't done anything beyond giving a quick try to any EDA applications other than Kicad and Eagle, so I can't say whether there are other options. Maybe someone else here on the forum will be able to provide a better answer.