I recently visited Tokyo for the first time and stayed at the Hotel Avanshell Akasaka in April, 2012 for about 14 days. I travelled with a friend and we had a large room with two twin beds, washroom with tub/shower, small dining table, desk, microwave, bar fridge and sink. I found that the rates were very reasonable. I brought a netbook and was able to connect with their free internet (they provide the cable if you ask for it) with no problem and use Skype to connect with people back in North America. They also provide toiletries, free toothbrushes, brushes, slippers and robes for your use (not to take home). We selected this hotel based on reviews from Trip Advisor and also wanted to be close to friends who lived in the area. I loved the hotel room!
The location was convenient to the metro, both the Akasaka station on the Chiyoda line (exit 2) -- about 3 minutes away and the Tameike-Sanno line on the GInza line. Although the Tameike-Sanno station is about 6 min away, it is sometimes easier to take to it to eliminate transferring. If you will be using the metro, we found it best to buy the PASMO card, load it with money and you're set to go.
In terms of eating around the hotel, as other reviewers mention, there are many places to eat. For breakie, there is a Starbucks north of the hotel (I think in the Akasaka SACAS building area) just north of the hotel (through the laneway) and also a McDonalds, Burger King in the same area. There are also nice cafes -- Excelsior and Tully's which have breakfast specials. If you want to try a cheap Japanese breakfast, try Yoshinoya's nearby. You get rice, salmon, miso soup for about 580 yen. There is a really good food market called Maruetsu Petit, which sells packaged food like bento boxes, sushi and fresh fruit, bottled drinks etc. We ended up buying a lot of food from this place. In the area, we also ate at Osteria Pippos? - in the hotel and it was very good. Otherwise we were out and about and didn't eat in the area much.
Although this may not be the cheapest way to get to the hotel, it was the route we took. To get to the hotel from Narita airport, we took the Airport Limo bus to TCAT station, which was about 6,000 yen for a return ticket and two days of travel on the metro. I think it was about a 50 minute ride on a very nice bus. Because we didn't want to lug the suitcase on the metro, we then took a cab from TCAT to the hotel. Since it's hard to describe where the hotel is, you can tell the driver that it's near the Akasaka SACAS or BIZ building and then walk from there.
For shopping and site seeing, you'll need to hop on the metro.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.