Finding pet-friendly hotels in Europe is not a problem. And it’s not in the US where a lot of hotels are either low-end and/or on the outskirts of towns. I tend to use booking.com which has a box you can tick for “pets” when you search for hotels.
Fritz and I have stayed in some great places. Our favourite is Hotel du Pillon, in Les Diablerets, Switzerland.
In London, we love the Citadines chain of self-catering apartments. The point is – yes, some hotels don’t allow dogs, but plenty do. Your dog should be crate trained, though. It’s a good idea, and required by hotels, to keep him crated when you’re not there. Also a lot of hotels charge a bit more per night, around €10/£10.
There are also some hotels that specifically bill themselves as pet friendly and/or designed for dogs. We’re looking forward to visiting these in future journeys.