This app was mentioned in 1 comment, with an average of 3.00 upvotes
there is an app you can download called Ramen map:
https://play.google.com/store/apps/details?id=jp.ramenmap.ramenmap
It's all in japanese but basically all you need to know is the red markers are highly rated restaurants and the rest are not worth your time (definitely not for 10 days anyways).
In any event, it is very popular for ramen shops to have a vending machine that you buy a ticket from. These don't always have pictures. So my recommendation is just to press the button that says "ラーメン". that is how ramen is spelled in katakana. If they can't do the basic ramen good, why go there at all?
Also, I have noticed that a lot of restaurants in Tokyo get quite popular for reasons other than their food being good. English language guides don't always pick up on this. So sometimes highly rated places aren't actually all that good. They are just expensive.
When will you come to Tokyo? I can take you to my favorite Jiro style ramen place when you are here if you want.