I traveled solo to Tokyo while Typhoon Ruby was in Manila. Took the Willer Express overnight bus from Osaka and stayed at the Kadoya Hotel, a small hotel in the Nishi-Shinjuku business district. Chose Kadoya for the price and location. It's near the Shinjuku Station West Exit, so the area is quieter compared to the chaotic entertainment streets on the other side of the Station. It's also a few steps away from the Shinjuku Post Office (for your postcard-sending requirements), 2 branches of Lawsons, and a Pronto Bar & Cafe that opens early (had breakfast there once when I woke up at 6:30 AM). Also, the Willer Bus Terminal (Sumitomo Bldg) is within spitting distance.
Like my last trip, I dined at Sushi No Midori at the Mark City Mall, Shibuya. Ordered the Chef's Special (app PHP 1,200) and had the time of my life. I will definitely keep going back whenever I'm in town. Other sushi places I tried are Numazukou (right under the Shinjuku Station West Exit; kaiten sushi, PHP 1,000 budget) and Sushi Zanmai (left side when you use east Exit 15 of Shibuya Station via Hikarie Mall; chirashisushi at PHP 570). Both are good, but Midori reigns supreme.
For katsu, I went to Hamakatsu near my hotel and had the Mixed Chicken & Pork Cutlet with Fried Veg set for PHP 450. For yakiniku, I had dinner twice at Jonetsu Horumon (Omoide Yokocho, the narrow yakitori alley northside of Shinjuku Station). They have an english menu, I recommend the beef rib. A meal cost about PHP 1,000 (2 plates of meat, medium rice, peach juice). For ramen, well, skipped that again. I don't like ramen very much.
It was a comfortably cool 6-8 degrees, so Coldstone and Godiva's Dark Chocolate Decadence cold drink were no problem. In the evenings, I had warm cups of Snow Maple Toffee Latte from Starbucks.
I did a LOT of walking and eating, some shopping, and visited two cat cafes - Hapineko in Shibuya and Calico in Shinjuku. Super cute chubby cats! And I'm not even a cat person.
I only wandered into Kabukicho in the mornings.
Fun trip!