A few things:
1) For cheap, great eats, conbini food is a great choice. If they are not adventurous eaters or have dietary restrictions, they should google "conbini onigiri" and keep a list of what the kanji mean on the labels. On my Japan trips, even with a more flexible budget I usually eat at least one meal a day at conbini, where you can get by on 500-800 yen (or less) for that meal.
2) I second jib71's advice to focus on a region or two- for example Tokyo + south (Mid/Southern Honshu and Kyushu) from my personal experience could easily fill a 20-22 day itinerary, plus the bonus of less time "wasted" traveling from place to place, though there are beautiful sights to see from trains. However, I understand some people have a "one and done" mindset with countries or that they'd rather "check the boxes/hit all the sights" then spend more time getting to know a place, but I echo LapLap to ultimately focus on their priorities.
3) They should understand that if they stick purely to local trains they don't get the essential (IMO) shinkansen experience, though using different modalities of travel in Japan is an important cumulative experience in and of itself. If I were to choose things to "splurge" on it would be at least one shinkansen trip, at least one night in a non-minshuku (so something closer to mid-range) ryokan, and some good (doesn't have to be high end) culinary experiences, especially local specialties.