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Stay at the Casino where you plan to play the most. Make your hotel booking through the poker room and you can get a discounted rate.
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This is great advice once you have been there and know where it is you enjoy playing.
For your first trip, especially since it is likely coming from Denmark that you will stay 3-4 days or more, it would suck for you to be tied to a room for 5 or more hours a day that you don't really like.
Instead, I suggest at a hotel that gets you good location at a rate you like and then feeling free to play wherever you want.
Take a look at
Cheapo Vegas for hotel descriptions, which include info on the poker rooms (granted not a s good as what you might find here) and use the
their map of the strip to get a feel for where the various properties are. Keep in mind when you look at the map that the Wynn is 5 kilometers from Mandalay Bay.
We can certainly help you more if you tell us what is important to you and the people joining you: poker limits, hotel luxury; how much you want to spend on a room; other things you plan to do; if you mind renting a car, or if you plan to drink the whole time, etc.
Edit All that being said, KCFire makes a very strong suggestion.
AAA, an American travelers advocacy group, rates hotels and restaurants in North America and the Caribbean. Only 85 hotels and 57 restaurants restaurants get their highest 5 diamond rating. The Bellagio hotel and two of its restaurants earned that rating. Plus, the Bellagio is always on people's short list of great card rooms here at 2+2 (along with Mirage, Wynn, and MGM).
If you and your friends like the poker room rate, you won't be making a mistake staying and playing there.