I do not think that budget will buy anything close to a high end hotel for eleven nights in those cities. If you could increase that budget somewhat, you might be able to stay at a high end hotel in one of those destinations, if you scaled back on the other destinations.
What about traveling in Eastern Europe? You currently want to go to some of the most expensive cities in the world for hotels. In Paris and London luxury accommodation can easily exceed $1,000 per night.