There are many various kind of bars in Golden Gai.
So I think that it is quite difficult to say which is the best bar.
I think that it is better to walk in the Golden Gai, ask a bar that is door open directly, and ask whether to you can get in.
Recently many non-japanese visitors are there. Maybe you can enter some bars.
I have never been to Omoide Yokocho, but I guess bars on this page with English descriptions would allow non-Japanese speaking visitors.
For Golden Gai, I have been to only one bar and I saw few non-Japanese speakers there. Unfortunately I forgot the name of the bar.