You can always get a decent lunch for 1000yen or less, only really fancy places charge much more than this.
For dinner, if you want to save money then there's plenty of options within Japanese cusine, like cheap sushi chains (1000-2000yen for a meal), grubby local eateries found in backstreet (Yokocho) (probably 2000 - 3000yen). And then there's the more famous cheap Japanese chain restaurants serving dishes like Gyudon (beef bowl) or donburi (something on rice) in general, grilled fish and meat. For example Ginhachidon, Otooya, Yoshinoya, Matsuya and Sukiya - these places usually cost no more than 1000yen for a meal.
If you're not on a tight budget, then there's still a huge amount of amazing eateries where dinner will cost less than 5000yen. As a general tip, for best cost performance, stick to Japanese cuisine and avoid flashy new looking places.
Also, we did a podcast on (cheap) Japanese cuisine: