Most beautiful -
1. I have to agree with the Gates Pass suggestion. I would expand it a little though to include the amazing trails near Gates Pass that allow you to climb to some of the most amazing views.
2. I also think most of Mt Lemon would also qualify though.
3. Sabino Canyon and 7 Falls as well. Both are amazing.
4. In the city proper, El Encanto is awesome and so is the Barrio area just South of downtown.
5. San Xavier. What's not to love about a several hundred year old Spanish Mission in your back yard?
6. The University of Arizona Campus, particularly in the area of Old Main and the other old areas of campus.
Most unique -
1. Casa Video is really cool.
2. I would also add the "Diner in a Train Car" off of Valencia Road. It's an old passenger rail Dinning Car that's parked out in the desert and now serves as a little restaurant. Good food, cheap, and very unique.
3. The Arizona-Sonora Desert Museum is one of the most "unique" places on Earth actually. Amazing place and a must-see in Tucson.
4. 4th Avenue. There is something remarkably "gritty" and real about the West University Neighborhood area. Cool shops, eclectic people, etc...
5. San Xavier. Yeah, I know I am listing it twice, but it really is both beautiful and unique.
6. Desert Survivors Plant Nursery on West Starr Pass Blvd. Not only do they have a great selection of native plants and smart staff, the money goes to charity. A very cool place.
7. Overpass Cafe. A big breakfast for $3.50 and the owner serves your coffee. Everyone is very friendly, the food is great and CHEAP and it's just a neat little family-run business.
8. El Charo. The oldest continually operated family owned restaurant in the United States.
9. The Flandrau Science Center and Planetarium on the UA campus
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Just a few places that come to mind... 