To help you out, I've scouted five spots across Tokyo, Osaka and Kyoto that are worth a visit if you want to see some of Japan’s top food establishments at low prices. So without further ado...
Tokyo
Nakajima
Sadaharu Nakajima is the third in line of master chefs, carrying on the restaurant after his father. Their specialty? Owan and sardines. Simply translated, owan means "bowl," but from Japanese culinary tradition, it is a type of soup typically associated with kaiseki cuisine. As for sardines? There are certain foods you might think of if you imagine haute cuisine or Michelin Star worthy eats, but a menu based around a soup and the humble sardine might surprise you. It is the perfect execution and ability to bring out the best in both dishes that makes this place worthy of its Michelin star.
The lunch sets here are incredibly inexpensive (under 1000 yen), so it makes for a popular, memorable lunch spot. Since it's a busy establishment, it’s very possible if you’re in a party of one or two that you’ll be seated with another couple of strangers, but the food makes it worth it.
The sardines are served in lunch sets in several different ways, from sardine sashimi through to sardine tempura and, of course, a sardine owan. As well as the sardines as the star of the show, your set also comes with the standard teishoku sides of rice, pickled vegetables, and miso soup.
A note of caution, though: even though their lunch menu is dirt cheap, their dinner menu is strictly kaiseki style and will set you back over 10,000 yen (about $100 US).

Tsuta
How does a ramen dish earn a Michelin Star, exactly? After all, ramen is seen more as a comfort food or cheap staple food (just ask any college student from the past twenty years), but Tsuta broke the mold by showing the world that it could be a delicacy worthy of food's highest rating.
One of the keys to Tsuta is that every element of it is exceptionally thought out. From the soybeans that are matured for two years in Wakayama Prefecture to make the soy sauce for the shoyu, to the noodles that are made at the premises, and the perfectly umami broth that is comprised of chicken, clams and various herbs, no step of the way is left to chance. Tsuta's shoyu soba is then topped with a slice of chashu pork, some leek, and truffle, which all blend together harmoniously. They also serve shio (salt)-based and miso-based ramen dishes here, and a range of sides.
If you like ramen, this is the spot for you. I especially recommend their signature dish here--the truffle oil blended Shoyu Soba. The ramen will set you back anywhere between 1000 and 1500 yen.

Fukamachi
Masao Fukamachi started as a chef's apprentice at 18 years old. At that young age, he started at the Tempura restaurant inside of the "Hilltop Hotel" in the Ochanomizu area of Tokyo, which was a hotel known for its high end restaurants. After nine years, he rose to the position of head chef of the hotel's small tempura restaurant, and there he remained for twenty-five years. At the age of 52, Fukamachi left the Hilltop Hotel to open his own Tempura restaurant, and it was not long before the world recognized just how special this chef's fried food really is.
Fukamachi earned his Michelin star by offering consistent, evenly battered and perfectly delivered tempura, and the trick to eating here on the cheap is to go without a reservation. If you do make a reservation, the three set lunch choices range anywhere from 7000 to 9000 yen, which is a little eye watering even though this tempura can hardly be matched. If you turn up on the fly on the other hand, one of the lunch menu options is tempura donburi--tempura served over rice--at a much more wallet friendly 2500 yen. Plus, to me, anything served over rice earns added bonus points!
If you have a perception of fried foods as nothing but greasy, weigh-you-down junk, the tempura here will challenge that notion--it’s cooked to perfection and will leave you with a new appreciation for the art of frying food.

Osaka
Naniwa Okina
So how does Naniwa Okina do it?
They offer up two different types of the noodles. They have nihachi (literally 2-8) soba, made from 20% white flour and 80% buckwheat flour, and jyuwari ("100%") soba, which is made from 100% soba flour. The jyuwari soba is limited to 20 servings a day, but is only an extra 200 yen--and the meals here are already great value for money. Their specialty dish is the zaru soba (served chilled), which will set you back a mere 900 yen for the nihachi soba noodles, or 1100 yen if you’re lucky enough to be one of the first 20 people who ask for jyuwari soba. Even the most expensive dish on the menu--their summer unatoro soba topped with eel and yamaimo ("mountain potato") paste, is set at 2500 yen (nihachi soba)/2700 yen (jyuwari soba) noodles.
For ease of ordering, they have an English menu in PDF form that you can access here if you’d like to plan what you want to order ahead of time.

Kyoto
Sobaya Nicolas
Sobaya Nicolas's buckwheat flour is sourced from Ibaraki Prefecture, and the master chef grinds the portion needed for the day's noodles by hand with a stone grinder (if that’s not precision and dedication, I don’t know what is). Best of all, a dish of the zaru soba (chilled) noodles here is 980 yen, but you can get a set with three assorted small-plate dishes as well as the soba noodles for 2160 yen.
