Yeah, they’ve priced the rail pass so you need to do some math first to see whether it’s going to be worth it (prices can be had by checking planned rail trips using Google Maps). If the OP is on a guided tour, then my guess is it probably won’t be worth it, especially if he’s not going on at least a few long Shinkansen trips; the bullet train is where the rail pass can really pay for itself.
If you’re into shopping/browsing experiences, here are a few for your consideration:
Electronics: Look for Bic Camera or Yodobashi Camera. Kyoto has both within walking distance from Kyoto Station. Osaka has Yodobashi Camera within walking distance of Osaka Station, and Bic Camera is down south near Dotonbori. Each store has many floors with an insane selection of electronics and home appliances. Not sure where they are in Tokyo, but Google Maps is your friend.
Household goods: look for Tokyu Hands. They have several sizes of store; the largest one I’ve seen, near Ikebukuro Station in Tokyo, is like Home Depot, Dick’s Sporting Goods, Bed Bath & Beyond, and Hobby Lobby all rolled into one. Camping gear, craft supplies, kitchen wares, tools, you name it, they had it. Something there for everyone; my wife browses kitchen wares and other areas, and I tend to wander around the tools and craft supplies. Lots of interesting things you won’t readily find in the US. They also have a fairly large store in the Osaka Station South gate building, and another a few blocks north of Dotonbori (Osaka).
Department store basements have already been mentioned for their vast basement food displays. In Tokyo, you might check out Mitsukoshi in Ginza. This place has the added bonus that if you do want to buy something to eat, you can carry your goods up to the (I think) 11th floor, where there’s a rooftop garden with tables you eat at, and (equally important) trash cans for discarding the packaging. You can also buy beverages in the basement, or up on that 11th floor. In Kyoto, check out Isetan at the west end of Kyoto Station. In Osaka (station), check out Daimaru in the South gate building, Hanshin just south of there, or Hankyu just east of there. If you buy something, you may be able to eat it in the Southgate building at the Taiyo-no-Hiroba, a sunny deck on (I think) the ~16th floor - or you can go to the Northgate building and look for the Kaze-no-Hiroba, a similar outdoor plaza with benches and a few tables. Can’t guarantee the availability of trash cans at either place, so you may want to check on that first.
Which brings up another point: public trash cans in Japan are in extremely short supply. Before you do anything that generates trash, consider that you may well find yourself carrying that trash all the way back to your hotel room.
All of these cities have blocks-long covered shopping arcades. In Kyoto, look for Teramachi, and branching off of its south end, Nishiki Market (the latter is more about food). In Osaka, there’s a whole complex of arcades around Dotonbori. To the north, Shinsaibashi has a lot of fashion stuff, but to the south there is Ebisubashisuji, which has more restaurants. Douguyasuji, a block or two east, has a lot of stores that sell equipment for restaurants - everything from cups and plates to major kitchen hardware. Several blocks further east is Kuromon Ichiba - a lot more food here, including a couple of proper grocery stores that make for interesting browsing.
Take some time to walk around in Kyoto Station and Osaka Station. These are enormous buildings, and in both places you can take escalators and/or stairs that will put you on the rooftop for a nice view of the city. In Osaka, you might also consider the 1/2-mile walk over to the Umeda Sky Building, where the span between two towers is occupied by an observation deck, giving you 360-degree views of the city.
If you’re a baseball fan - or even if you’re not - consider attending a Japanese professional baseball game. The level of enthusiasm is more like a European soccer match (without the hooliganism); an American baseball game is sleepy by comparison. It can be challenging to get tickets online beforehand if you don’t read Japanese, but if you can pull in a favor from a Japanese-speaking friend, it may be worth it. The Hanshin Tigers home field is Koshien Stadium, a short train ride from Osaka Station.
If you want to get up close and personal with a troupe of Japanese macaques, visit Iwatayama Monkey Park in Kyoto. It’s a good 20-minute walk up a hillside, but you’ll be out there with the monkeys (don’t touch and fergodsake DON’T stare), and you can also enter a caged area where you can feed the monkeys (which are on the outside of the cage).
If you’re a pre-planner, Google Maps is a great resource for figuring out which trains to take, and which stations to get on/off at (and also how long it’s going to take to get somewhere). A cell phone is also a handy resource, even without cellular service. When you’re using wifi in your hotel room, scroll around on the map so it downloads all of the detail in the area; then you’ll have it as a navigational reference when you’re out and about (you can also connect to wifi at many restaurants and coffee shops). It’s sometimes very useful to know that the train station or tourist attraction you’re trying to reach is just one or two blocks over.
A few worthy cultural attractions in Kyoto (not a comprehensive list):
Kinkakuji (“The Golden Pavilion”)
Ginkakiji (“The Silver Pavilion”)
Kiyomizu-Dera (plenty of touristy shops on the way back down the hill to the NW)
Fushimi-Inari (famous for the gazillion orange “Torii” gates that line the loop trail on the mountainside; nice view of Kyoto from that trail)
Sanjusangendo (a LOOOONG building filled with 1000 life-sized statues of the Buddha)
The aforementioned monkeys are in Arashiyama, which has plenty of other things to see and do. Check out Togetsukyo bridge (you’ll cross it to get to the monkeys), and also the walk through Sagano bamboo forest. Plenty of touristy stores and restaurants in the area, and a few temples/shrines.
If only have a day or so free in each city, I would avoid making long out-of-town field trips, as you’ll end up spending a good percentage of your time on the train. Hiroshima, for example, is about two hours each way from Osaka; the atomic bomb museum and peace park are significant, but given how limited your free time is on this particular trip, I’m not sure it’s worth spending four hours in transit for that alone, as doing so rules out doing a lot of other stuff Osaka/Kyoto.
