Hey! Nice question! I think others will benefit from this, too. Here are a few of my suggestions.
Budget: Youth hostels and capsule hotels. Avoid big names like Hilton, etc.
Food: Yoshinoya, Sukiya, Matsuya, kaiten zushi (conveyor belt sushi)
Things to do: plenty of free festivals year round, free parks, etc. If you want to go to karaoke, go in the daytime at weekends, it is only a few hundred yen. Avoid the cinema as it’s around 2000 yen per head.
Shopping: UNICLO and Forever21 are good shops. Also check out Harajuku’s Takeshita street (NOT at the weekend – it gets really crowded) for discount shops and bargains.
Hope that helps, and have an awesome time in Japan!