I agree that early June is likely to be rainy and not the ideal time for outdoorsy trips like Mt. Fuji. This may be one of the periods when you can be ten miles from it and not even know it's there. If it's visible at all, it will be visible from the 45th-floor observation area of the Metropolitan Government Building near Tocho-mae subway station.

Laundry has never been a problem for me in Japan. The Tokyu (not "Tokyo," "Tokyu") Stay apartment hotels, for instance, have free washer-dryers in the rooms. Some of the business hotels have coin-operated washer-dryers and detergent dispensers for guests. If not, ask at your hotel where the nearest "coin laundry" is.

You sound like a good candidate for the Suica-N'Ex ticket combo, which gives you the Narita Express into town plus a rechargeable Suica debit card for riding subways and surface trains.

A plastic fork and spoon should be sufficient if you want to try Japanese food, since it's normally cut into bits suitable for eating with chopsticks.

Be aware that Japanese-style curry is eaten with a spoon anyway, so you'll be safe at curry houses. There are also an abundance of Western-style and every other style of restaurant, not to mention fast food places, all over the city--McDonald's, KFC, Mr. Donut, and homegrown chains such as MosBurger and Lotteria.

In recent years, good Italian, Indian, and Thai food have become more easily available, a real change from the 1970s, when "Western food" might mean spaghetti stir-friend in ketchup and the Thai students at my university were pining away for lack of spices.

Shinjuku is a good area to stay in, since it's a major transportation hub, and crowded, confusing, labyrinthine Shinjuku Station, said to be the busiest train station in the world, is an Experience. But don't be intimidated. Just get a good map and guidebook and follow the bilingual signs.