A good question and one which deserves a good answer. That building is across the street from an American School in Japan (ASIJ) bus stop so not too bad by the standards of the folks that send their kids there. It is also next to a spot where a new supermarket is opening soon. That part of Roppongi is just fine in many respects. If you are walking from the crossing to the Hob, you will indeed encounter the seedy side of Roppongi at night. There are pluses and minuses that will be increased or decreased depending on where you are walking to/from and whether or not you will be driving.
Will you be working in Roppongi? In Roppongi Hills perhaps? If so I would look closely at the areas of Nishi Azabu which is entirely different from both Minami and Higashi Azabu areas. Or even Moto-azabu for that matter. I would consider Hiroo for sure as it is quiet but rather boring. What you really need to do is establish what your budget is, how close you want to be to work/play/food shopping/restaurants/subway/etc. Then you would be well advised to contact both KEN Corporation and Plaza Homes. Both of these have extensive experience in the areas you describe and with non-Japanese tenants. They will be able to prepare a spreadsheet showing a comparison of available units at your price in all areas. They will then take you to each in their car and make sure you have all paperwork handled appropriately. They will also be able to intelligently discuss the merits and demerits of each place they show you. I can do this with you also, but as I work for a single developer my views of what is good and not may be slightly biased. I do however have 10 years in the field at Tokyo’s biggest private developer so you are welcome to ask questions here or via e-mail. I have a fair bit of information and I am always happy to help a fellow FTer.
Mike