Why don't you just look at the hotel chains you are interested in and see what properties they have in places you are thinking of visiting? My experience is that availability of properties differs a lot from country to country and from chain to chain, so there's not much point in generalizing.

One caution is that most U.S. chains are rather business oriented and their hotels in Europe may, therefore, not be convenient for tourist purposes. I still regret Hilton having ended their association with Scandic, as my stay at the Scandic in Brussels (for 10,000 points a night, at a hotel one block from the Grand Place) was among my best uses of hotel points ever.