I always found just leave it on auto and let it do its thing
Honda aircon isn't the best and in summer on hot days I dropped the selected temp to 19 which seemed to do the trick and dropped the temp to 21 ish, eventually. Setting 21 and the temp never got below 24
On my previous Lexus IS200 and Xantias, if I selected 21 then it went down to 21, and quite quickly as the fan gave it some till it got there. All read from an accurate internal digital thermo I had. Positioned out of sun and car airflow
Honda system (3 Civics and the Jazz) seems weak and gives up early. Maybe down to striving for better economy figures