SnogTar, they're all in Yoyogi Park on Sundays now. They get hassled somewhat, but if they weren't in the park they'd be somewhere else, so I figure there's a certain pragmatic policing/noise generating balance.
ANA Akasaka is nothing special. 5 minutes from Roppongi, 5 minutes from Akasaka but although it's a bar/entertainment district, it's not a tourist bar/entertainment district. If you're after boozing and other recreations in your own language, then at some point you'll want to try out Roppongi. If you want to see electronics, major department stores, greenery all in one day on foot, then it's Shinjuku. Akasaka for vast amounts of electronics. From Shinjuku, you can be in Akihabara in 16 minutes, Shibuya in 5, Roppongi in 9 on the various rail and subway links. I'd to Shinjuku over Akasaka. If you want Akasaka on Park Hyatt-style money, then I'd stay at the Okura Hotel. But, on that type of money, I'd just do the Ritz in Roppongi!
The wife will get a lot out of Shinjuku, if she's shopping oriented. With 7 days, you can check out Shinjuku, get a train to Yokohama and/or Kamakura, if you're brave get a train out to Takao (closest "mountain" to Tokyo), for a LONG day go to Nikko (I'll blaspheme and say it's not worth it unless you're REALLY motivated). Ginza's seen better days but it's still worth a look. Try all the food you can find. Unless you need a big western-sized room, I'd probably go for something at the Odakyu Century Southern Tower Hotel: middle of Shinjuku, good views, spend the money you save on restaurants and goodies. You could walk 10 minutes in any direction from there and be somewhere interesting, or be anywhere in the city in 30 minutes.