This is one of the larger issues facing yoga today. Much of what is being taught is not yoga but rather asana. And, of course, asana is a tiny sliver of yoga.
In Purna Yoga™, the yoga in which I train, teach, and practice, we teach four elements; asana/pranayama, meditation, lifestyle/nutrition, and applied philosophy. This might suit you though as teachers we are spread thin. (Where are you located??).
Gordon is right that all Yoga styles incorporate the elements you are seeking, though if you are not looking to explore flexibility in too much depth then a "Restorative Yoga" might be the best approach. Many yoga studios will provide an introductory or beginners yoga sessions as well which is a good start.
Yoga is all about exploring the dimensions of your body with rhytmic movements or sustained holds, in conjunction with deep breathing and a focal point in each posture (asana). I would recommend you also explore Tai Chi or even Qigong which are both fantastic absorptive meditative expriences with slow rhytmic movements.
Wishing you all the best in your personal practice
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