As the 1st name of the Hilton founder Conrad Hilton, Conrad brand hotels do not even have a presence in 1st tier market such as New York, LA, SF or Paris.
In Asia/Pacific, Conrad has a top tier location in HK, next to the Shangri La Island HK. It has a interier entrance to the Pacific Place mall in Central and commute to Exchange square on MRT is a breeze. Very easy to taxi to 兰桂芳 after work. Some suite/room have nice view to the mountain and harbor. Room size and service are good by HK standard. Stayed at both many times, I would think most travelers will rate Shangri La higher than Conrad.
Conrad in Singapore and Tokyo have nothing to write home about.
I don't know much about the Conrad in London.
Frankly I think Conrad could compete with Park/Grand Hyatt or the Westin as a premium biz hotel. It is not in the same league as Four Seasons or even Shangri La.