I lived in Takanawa for two years, actually. The Ishimaru grocery store next to the entrance of Shinagawa station (the one closest to the Takanawa Prince) often has excellent prices on whisky, but don't expect a vast selection. From Shinagawa station you can go to Bic Camera in Yurakucho, which is about 10 minutes away on the Yamanote Line or the Keihin-Tohoku line. It is a huge electronics store with a nice selection of whisky. A better bet would be to go to the Kawachi-ya liquor store in Shibuya, which is 13 minutes away from Shinagawa on the Yamanote line. You'll have to walk through Shibuya for a few minutes to get there, but it has a superb selection of scotch and bourbon with very low prices. Hit me up with a PM and I can give you more detailed directions, as some of the shop signs are in Japanese.
don't be afraid to check out the basement-level liquor shops in some of the nicer department stores around tokyo, such as Isetan in Shinjuku. The prices are always a bit high, but you'll have a better chance of finding some single cask offerings from Japanese distillers there than in the other shops. For standard bottlings, Bic Camera will treat you just fine.
For a bar, Helmsdale is probably the closest dedicated whisky bar to Shinagawa Station. You would again take the Yamanote line, this time to Ebisu (about 10 minutes away). From there you can either walk or take a taxi to Helmsdale. http://www.helmsdale-fc.com/helmsdale-map.html
It is an easy place to miss, given its non-descript exterior and location on the second floor.
How long will you be there?