I have two days of vacation before a conference in Scottsdale, Arizona and I'd love to spend them biking in the area. For (single day) biking trips in the nature, what are the pros and cons of each place?
It depends on whether you want relatively flat trails or mountain biking, as you didn't say.
The Scottsdale Green Belt is a paved trail several miles in length that begins just north of Shea Boulevard and ends in Tempe. There are only a few places on the trail that require crossing a street, as there are lots of tunnels that pass below busy streets.
There would be dozens of hotels located along this path, ranging from simple motel-like accommodations to pricey resorts. Here is a map of the path and various connections.
For mountain biking, I recommend South Mountain in Phoenix which is the largest city park in the world. There are more than 10 different trails in South Mountain ranging from 1 mile in length to 14 miles (58 miles total). Difficulty ranges from moderate to difficult. There are also several hotels/resorts in the South Mountain area. You could also check for accommodations in the Ahwatukee area of Phoenix just south of the mountain.
Note that it is just starting to warm up here -- late April and it was over 100 °F (38 °C) here today (I live in Gilbert, just SE of Phoenix). The forecast for next week is mostly high 90's to low 100's °F (35-40 °C); it's just going to gradually get hotter. So take LOTS of water with you.