We recently stayed four nights at the Bonham in early April, and were very happy with our experience. Located in the New Town, quite near Dean Bridge, it was about a 10-15 ride by taxi from Waverly train station, depending on the traffic. It's situated on a very quiet street that offers a little shelter from the hustle and bustle of the city. The lobby area doubles as a lounge; check-in was quick and professional, and we were shown to our room promptly. The place is nicely decorated, with some interesting lighting touches in the public areas.
The room was large, clean and very quiet, with thick drapes that foiled light and sound: when closed, we could scarcely believe we were in a large city. Even when the hotel filled up with traveling business persons and even hosted a conference during the week, it was a very welcome and relaxing experience after a very long transatlantic journey. All the furnishings were very comfortable, especially the full king-sized bed and the wheeled easy chairs that we could draw up easily to either the window or in front of the flat-screen television (which has a free web-TV feature that could be very handy for anyone traveling without a laptop computer, but it was not easy to navigate the web with it).
The hotel restaurant menu offered an interesting combination of traditional and modern, a welcome change from the usual Scots-French fare common throughout the city. We enjoyed dinner there once, and room service on several occasions. A word about the room service: impeccable, and quite possibly the very best we've ever had traveling anywhere in Europe.
Walking to Princes Street and the main part of the New Town was easy, about 10 minutes at most. Reaching the Royal Mile on foot was a little more challenging and takes longer. You could walk all the way around the west face of Castle Hill and up to the Mile from the south side, but a more picturesque route is to walk to Princes Street and either walk up the Mound or stroll through the Princes Street Gardens. Depending on whether or not you're a quick walker and get easily distracted, allow for at least a half hour by these routes (the same for walking to Waverly Station along Princes Street if you're carrying luggage).
Altogether we were impressed with the hotel and staff, and we'd be happy to return.