Completely random thoughts:

If the kids are anime fans, keep in mind that the TV in your hotel room might be worth a look. Of course, it will not be in English but still worth a look. Some hotel TVs have bilingual capability but I don't think the anime shows are set up for it. Also, trying to decipher the morning weather forecast from the little on-screen graphics is "interesting." Memorizing the kanji for "Tokyo" will help.

June is the rainy season so be prepared to do at least some of your touring in rain gear and/or umbrellas.

I dislike dining at lzakayas because of the noise and crowds of regulars plus all the folks trying to see how much alcohol they can take in after work. I usually just go out and walk until I find a nice neighborhood restaurant or two that look good. The best mom-and-pop places tend to be off the main streets and in what look like alleys to western eyes. Look for lots of lighting and displays of food dishes or chalk board menus out front. If all else fails, there will be unremarkable but decent places near or in train stations. Department stores are also good bets but the best meals I've ever had came in little off-the-track neighborhood diners.

I prefer to get my larger meal of the day around midday, just after the lunch rush of office workers on limited lunch breaks. In the evening I have a light, "lunch-type" meal, often a bowl of noodles or sandwich. Having the big meal at lunch saves significant money as it is often the same food as the dinner menu but at a lower price. The daily lunch specials are always a good bet. I am pretty adventurous so it doesn't really matter what the special is, it will be good. If one or more of your teens will spend a couple of months learning Japanese kana - both hiragana and katakana - they will be able to read the little menu strips hanging in many small places. It just adds to the fun. Places that are used to tourists will often have an English version of the menu. Also, be sure to try a noodle shop for a big bowl of ramen at least once.

Your kids should browse through the snack and "bread" sections of any big convenience store, if only for the cultural experience, and drinks are cheaper at the konbini than from the zillions of vending machines. Plus, blueberry or green tea Kit-Kats are great! Convenience store food in Japan is MUCH better and of wider variety than here at home. And, of course, there are plenty of McDonalds, and other western places if you need the occasional burger fix, although Mosburger beats McDs hands down.

Choosing a hotel that offers breakfast buffet included also saves money and time hunting up a place for breakfast. Most low- and mid-range "business" hotels offer breakfast, wi-fi and coin laundries for those of us who travel very light.

I don't care for the Ikebukuro neighborhood for a 5-night stay. It sounds like you are settled on that hotel but I think Sakura has a property in or near Asakusa, which would make for a better "home" area. You might find something in your budget range that offers Japanese-style rooms (sleep on the floor, shudder) here: http://www.japanhotel.net/ . (Note - they seem to be down for some reason right now but I can vouch for their reliability.)

With teenagers along, I think the main Edo-Tokyo museum in Ryugoku would make for a very good use of a few hours. Just the covered multi-story escalator entrance alone is almost like a short Disney ride and the rest is educational while also being interesting and visually impressive. If you get lucky, there may be a craft or art show or free rock concert in the courtyard. When I took my two college-aged nieces several years ago, we caught a great free concert by an up-and-coming young band completely by accident. The sumo arena and museum is right next door but there is no tournament on during your visit. The sumo museum isn't much and I wouldn't make the trip just for that but it might be worth a quick look if you are already there.

For souvenir hunting, the outdoor Ameyoko arcade across the street from Ueno Station is fun but the Nakamise arcade leading up to Senso-ji temple complex in Asakusa is more fun, with tourists of every nationality mixing and mingling and the smells from the various food stalls activating everyone's salivary glands. Don't be afraid to try the street food. It will be safe and very good. As I recall, there is a big manga store in the cross pedestrian street running perpendicular to the main arcade that might interest your kids.