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This is an iconic National Park in Utah...so popular the Delicate Arch is featured on the Utah license plate. The hike up the rock face is some work but it's worth it! Be sure to check out Double Arch, where a scene from Indiana Jones and the Temple of Doom was filmed. Landscape Arch is also worth the visit...the span is so wide, a football field can fit underneath.
Pro Tip: There is lodging in Moab if you want to be nestled between Arches and Canyonland National Parks. However, many folks make the ~1.5 hour drive from/to Grand Junction, CO to have access to more options, including food.

Nosh:

Moab Brewery: Their sister company is next door, Moab Distillery. The pastrami sandwich is excellent. Nothing like tender beef and a side of fries to refuel after a long day of exploration.

Nip:

Moab Brewery: While at Moab Brewery for dinner, it make the fitting place for a nip. I went with the Squeaky Bike Nut Brown Ale. All the beers are creatively named so pick something and go for it.
Pro Tip: Utah state law prohibits samples (considering them free alcohol). Different breweries approach this differently, charging anywhere from $0.01 to $1.00 for a sample. Moab Brewery charges $1 for a one or two ounce sample so just decide what you want and commit.