comma with two introductory phrases [preposition]: In Sun City, at...

Hello,

In Sun City, at the end of the day, everybody used to get together to celebrate the summer.

Is it correct to put "at the end of the day" between commas?

If so, is there a technical explanation for that?

Thanks.

Commas are usually optional in sentences like this. They are there to break up the sentence in the same way that you would break it up with your voice while speaking.

I would have commas in the exact same places as you have put them.

Yes, this is very much a voice thing. A comma often indicates where you drop your voice a bit, or slow down. If you had only one of those, 'In Sun City' or 'at the end of the day', at the beginning of the sentence, you would be able to read it straight through without changing your intonation much. But with both there, you really have to pause.