There is a public city hall called ”那覇市ぶんかテンブス館” at the heart of the street named 那覇市国際通り. The English name for the street is Naha City Kokusai-dori St. You can see the image of the street in the link below. https://naha-kokusaidori.okinawa/assets/pdf/Official-Illust-Map-En-Kr.pdf ”那覇市ぶんかテンブス館” is also called "てんぶす那覇”. It looks like ”おでかけ！テンブスマイル” is a radio show that provides information at "てんぶす那覇.” 那覇 is spelt なは in hiragana. "おでかけ” is going out, or outing.

"テンブス" is an Okinawan dialect word that means navel. It also means center of something because the navel is located at the center of a human body. So I think "テンブスマイル" is a play on words on "テンブス" and "スマイル”. So I assume that it means something like the center of smile or very happy.

I don't know テンブスマイル means. I am guessing テンブ+スマイル(smile), but no idea about テンブ.