Here's my first attempt at a Riley! Good luck!
The thought of my prefix brings many a smile;
Sit down, relax, or sleep for a while.
My infix is, mathematically;
One point six times five point eight, then less three.
My suffix is a speech, mad and long;
Which definitely is not a song.
Answer
Restaurant
Prefix
Rest is a synonym for relax, etc. and people look forward to it wistfully, with smiles on their faces.
Infix
Tau (twice pi) is approximately $6.28$, which is $1.6 * 5.8 - 3$. Clued in by @Omega Krypton.
Suffix
Rant, which is an unhappy speech
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