Yes, the sentence "May today bring good tidings our way" is grammatically correct.
It expresses a hopeful sentiment, wishing that the day will bring positive news or good things to the speaker and those they are addressing. "Good tidings" is an older or more formal way of saying "good news."
Here are a few possible rephrasings:
1. "I hope today brings us good news."
2. "May we receive positive news today."
3. "Wishing that today brings us