Hi Georg,
You're in for a real treat. The American Southwest, especially Utah and Arizona, are home to some of the most beautiful country in the US. I live in Sedona, Arizona which is just 30 miles south of Flagstaff. It is beautiful Red Rock Canyon country and is one of the most beautiful places in Arizona. If you are going to Flagstaff it is worth at least a day's drive(I presume you're driving) down, ie south, to Sedona on Highway 89a which takes you through Oak Creek Canyon into Sedona, a very pretty drive. In Flagstaff, you might want to consider visiting Lowell Observatory. They have an active visitors program that includes an opportunity to look through Percival Lowell's 24" Alvan Clark refractor, the scope Clark used to discover Pluto. Here's a link to Lowell:
http://www.lowell.edu/Flagstaff is also home to RCOS and Brad is generally happy to show off the facility. If you have one of their scopes, you could go there and visit your money.
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If you don't have a RCOS you could visit my money.
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While Arizona is great, Utah is spectacular. You mentioned Zion and Arches National Parks. These are definitely worth seeing. Zion is in the southwest corner of the state and Arches is east-central, immediately north of Moab. The drive from Zion to Moab is wonderful and includes most of the places you will want to visit. Driving from Zion to Moab you will first come to Bryce National Park which is a must see. Then you travel from Bryce to Torrey on Highway 12. This highway is 124 miles of spectacular scenery. It is know as one of the most beautiful highways is this country. I driven it many times on my Harley and it is a breathe taking ride. I'm sure it won't be too bad is a car either.
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Here's a link to information about Hwy 12:
http://www.utah.com/byways/highway_12.htmHappy to answer questions if you like. Perhaps it would better privately. My email is sleshin@yahoo.com. And if you decide to come to Sedona I'd be happy to meet you and your family and show you around.
Cheers,
Steve