Something that can be frustrating if you're living in or travelling around Japan as a non-native speaker is the absence of English or picture menus. It can sometimes feel like the busiest and most popular restaurants with the locals are Westerner-phobic, or at least like the best food is kept hidden away.
I live in Osaka and I discovered this place, Kitarou Zushi, on a whim. Mention it to a local though, and they'll know what you're talking about immediately! It's quietly nestled in to the second floor of a large, loud, beatdown building named after a nearby temple in Amerika Mura. The building is full of small rooms, each of which is its own bar. I recommend wandering from room to room and seeing what sort of oddities each bar has hiding behind its closed door. Check out the My Little Pony-themed bar next door to the restaurant!!
Then, after 8 PM and before 6 AM (closed on Sundays), head to Kitarou Zushi for some of the best and most affordable sushi you've ever had in your life. The place is run by two brothers, so it's a family affair. A little Japanese goes a long way so show them this: あなたおしんらいします. (I/We trust you.) なんでもおたべられます. (I/We can eat anything.) Order a few beers or an oolong hai (spiked iced tea) and say 乾杯 (kanpai, or cheers) to the locals!
RECOMMENDED: うなぎかばやき (unagi kabayaki); かんぱちのかま (kanpachi no kama, or Amberjack Fish Collar); ほたるいか (hotaru ika, marinated whole baby squid).