The Good, the Bad, and the Ugly
Good: One side of the planet will be fundamentally uninhabitable. If you want the away-from-the-sun side to be habitable, move the planet closer to the sun. If you want the sun-side to be habitable, move it further away. In the case of your toroid, you'll have regions of the planet that are curiously habitable. For example, the sun-side may be too hot, but the sun-side center-of-the-torus might be just right, which means the other side of the inside will be warm, but likely habitable, while the far side of the torus might be too cold. You'll have sweeps of geography (cool, curving sweeps) wherein habitability is possible.
And I'm not even going to try to address the issue of climate on this world in detail. I suspect that if you land that planet smack dab in the middle of its ideal Goldilocks zone, the result will be a storm vortex in the doughnut hole that would impress even the angels in heaven....
Bad: But your real problem is that I suspect you're throwing science out the window (remember, you're using the science-based tag). I could be wrong, but I don't believe a toroidal planet could be tidally locked. Tidal locking kinda depends on the spheroid having a somewhat homogeneous-enough density that the forces can balance permitting the lock. Your toroid doesn't have that. Someone with a lot more celestial mechanics than I have will need to get involved, but I don't think your question has enough of a science-based foundation to justify the science-based tag.
Aaaaand the ugly... If we ignore the toroid as you suggest, then what remains is another "life on my tidally-locked planet" question. A bunch have been asked on this Stack, which would make your question a duplicate.... You sure you want to ignore the torus?
I just read @Halfthawed's answer. I like it and upvoted it. You should too. It does a good job of pointing out the one way a torus might, maybe, be tidally locked. However I'd like to beg to differ that the result would be an entirely uninhabitable planet. Technically Mars in in Sol's goldilocks zone, which would suggest you could move the tidally locked planet far enough back to permit its sun-side to be habitable. Maybe the consensus would be that it's scientifically impossible — but I believe it's well inside of suspension-of-disbelief possible.