What are good metrics to compare climates?
The Köppen climate classification is a classic metric to classify climates:

Source: Wikimedia Commons
It classifies climates based on the number of months with temperature below and/or above certain thresholds, and on whether rainfall is evenly distributed or concentrated in a particular season.  You will find details on the definitions on Wikipedia.
An alternative is the Trewartha classification:

Source: Wikimedia Commons.
Note that the climate you seek may not exist:

I was initially seeking to discover areas with a high mean temperature, low variance in temperatures annually and daily, and low rainfall.

A low temperature variance tends to happen in humid climates.  Dry climates tend to have large temperature variances.  A subtropical highland climate may come closest to what you seek, although it's not particularly dry.  In the Köppen classification, this would be Cwb.  From the Wikipedia article:

Cwb = Subtropical highland climate or Monsoon-influenced temperate oceanic climate; coldest month averaging above 0 °C (32 °F) (or −3 °C (27 °F)), all months with average temperatures below 22 °C (71.6 °F), and at least four months averaging above 10 °C (50 °F). At least ten times as much rain in the wettest month of summer as in the driest month of winter (an alternative definition is 70% or more of average annual precipitation received in the warmest six months).

I don't think any place with Cwb climate exists in the United States.  Quito is famous for being the city of eternal spring, and some areas of Mexico are classified as Cwb, as in Johannesburg.  I suspect the closest you'll get in the USA will be somewhere not too high, not too low in the Sierra Nevada.