Personally, I'd shoot for the smaller, brand-new apartment that's cheaper so that I could sock some of that extra cash away - or go out drinking more. Sounds like you're a banker, I'm not sure if your kind are able to have fun - I never met a single banker out while I was there, they were always having to deal with things like "stock markets" and "investments."
Seriously, though, in the words of one of my professors at TUJ (who advises expats and finds them jobs), if you can go smaller and sock the money away, that's the best way to do it. When he first moved there, they gave him a $6000/month housing allowance. He found a house outside Tokyo for $1000/month for him and his family - the company just gave him the $6000 and said "do what you will," which is apparently typical, I hear.
If you are looking in Minato-ku area, I found these people to have great services (FTTH, Cable, etc.) -
http://www.eg-wave.com/e/ and they were VERY efficient. I was in within one day of finding a nice 20m^2 in Akasaka with practically everything from a magical toilet to FTTH to a washer/dryer, and the place was a year old. I didn't have a magical view (although I could see OVER the next roof to the Mori Tower rising into the sky), but I had a little bit of one. (Remember, you're gonna pay more for a view, because those are typically in the skyscrapers, ne?)
Although, as a banker, you could just sleep in a cot in your office...
As for some other things - you should definitely get private health insurance, which will enable you to go to places like the Akasaka International Clinic (my preferred doctor) or the Tokyo International Clinic and not have to pay out the nose every time.
Furthermore, I know you do want to live close to your office, but if you're really about my age (25ish) you may want to look into some of the slighly further away "younger areas" like Shimo-Kita (amazing very chill area) or Ebisu (also fantastic. Actually, I just found this blog post reporting on the Best Neighborhoods 2007 -
http://smt.blogs.com/mari_diary/2007..._best_nei.html , you may want to read it.
Finally, just from my personal experience (and summing up some of my comments): I LOVED living in Akasaka. I went to school in Azabu-Juuban (20 minute walk) and worked in Yotsuya (2 minute walk + 2 stops on the train), so it was extremely convenient. But I can also say that as time went on, I kept thinking that if, after I graduated, I went back to Tokyo again, I would want to live further away from the center - it's amazing, but it's also super expensive & loud. While I could go out in Roppongi every night (and, sadly, did), I also started to want to get away from it more often (I ended up going to Niigata for mountains and hot springs a lot) and going out further away. YMMV, of course - I knew it was kind of time to get out of there for a little when I started to say to my girlfriend "kettai na gaijin wa akan ya naa."