You're welcome :) Just came back from a 3 weeks holiday there. I went to Hakone, dunno about this particular onsen though. Imo, as long as the Onsen has a outdoor bath you'll be happy :) also better to go at lunchtime if you want to be alone. Otherwise, most onsen are opened 24/7 except one hour a day to clean up (usually around 1AM). In Hakone, I recommend going uphill and then make a 2 or 3 hours walk. The vegetation was very different (although not exceptional) from the european mountains vegetation, so it's nice. Also don't expect a nice view of the Fuji, it's probably too wet to see that clearly (except maybe in the morning, very early. Better ask before).

In Kyoto, I don't know, for some reason I could stay only 2 days but my buddy said bike was much better than bus (bus is very slow). I went to the bamboo grove area, and to be honest the bamboo groove itself was disappointing, but the gardens in the area are awesome. I think one of the best thing in Japan are Japanese gardens. There are a lot (hundreds) in Kyoto, so best get a travel guide to help you chose. I don't know how to find an english group.

The dishes are pretty fun to eat too. You'll probably need some help to know how to eat them, don't hesitate to ask your waitress :) Also, for Okonomiyaki, ask to eat on the hot plate (the biiig cooking plate you'll be sitting in front of), and I'd rather eat the Soba (thin noodles) than Udon (fat wormy noodles) version.

Tokyo fish market: I haven't been there to see the auction. However, it's basically a markethall, with lots of trucks and people working, so if you've been to a market in Europe I doubt you'll be very surprised. If you're close, it's not really hard to wake up, take a peek and go back to sleep afterwards though. Entrance is free. There are Sushi Restaurants there, I've eaten there, it was expensive and although it was good, it was not exceptional. I don't know how the prices compare with normal sushi restaurants, so maybe it's not that expensive.

No problem with whipping it out, but if an english menu isn't available, usually there are plastic models of the dished serverd outside, so you can just point out and say "I want that".

Also, try Yakitori once. Yakitori are small kebabs, you eat them while drinking a beer and chatting around (warning, it's not a meal! Don't expect to go out of there bellyful). They are very tasty, a little expensive too. But soooo good.

In restaurant, you can ask for "osusume", the recomendation, the waitress will then give you advice. Also water or tea is usually free, so you don't feel forced to order a drink.

Final advice: you won't be able to withdraw money at most ATM because you have a foreigner card (even Visa or Mastercard, if it's from abroad it won't work). The ATM at 7&11 supermarket always worked for us though. These supermarkets are everywhere and are open until 11pm, so if you need money that's usually the most convenient place to go.