It took me a while to appreciate things in tea besides the taste, and how to perceive those things during my session.
Texture && Sensations: I had some Jinmudin recently and after the 2nd steep my mouth was completely numb and I was very relaxed. Shui Xian makes whole jaw feel heavy and it leaves some sweetness on my lips. Some shou mei makes my whole body tingle while making me feel like I'm on cloud 9.
Liquor Thickness && Fluidity: I love some sencha that has a thick liquor that feels weighty in my mouth but also I like tea liquor that moves around in my mouth like oil. Sometimes its like a small ball that rolls around and you notice it at the top of your palate and is quite noticeable.
Perceived Warming && Cooling: During winter months and summer months I like different teas because of the effects. I'm not going to mention 'qi' at all because it hasn't been properly demystified and explained to my knowledge. Yet we all notice mental and body effects during our time with tea.
These are some of the things that I value while drinking tea besides the taste itself.
What aspects do you value in tea besides taste?:
This thread has a related discussion of interest; Aroma vs body vs balance vs cha qi