I am on my 4th set of baby chicks and have my home-made brooder in the master bathroom!! I am sick of it actually, as much as I love them, I hate having them in the house.
I agree, you can put them right outside. If you have a draft-free, well insulated coop you can put them right outside with a lamp for heat and they should be fine. I did this with my ducks. I piled straw in the back so they couldn't get too far away from the lamp.
If your brooder can protect them from drafts and keep them warm, you can put them in a garage or shed or your basement.
I have 17 chicks in a large plastic tote in my living room, right here beside my computer desk LOL so I can see them and tame them and make pets out of them
Hubs doesn't care for them being in the house, but I love it.
now mind you, these ones are my hobby breeds, the Mille's, Silkies, Brahma Bantams, and Creoles. The dual purpose (meat and eggs) are raised outside.
Wherever you put them, just make sure it is safe from predators or your other pets (such as dogs or cats). You could certainly use some chicken wire to partition off a safe area for them in the regular coop if you have electricity out there to run the brooder light.
I have mine in our garden tub in one of the bathrooms. Im using the curtain shower rod to hold the light. Its very easy to move up or down as needed. They seem to be doing great.
You can put them anywhere you want them, as long as its preditor proof, draft free, and able to keept warm enough for the chicks. No Chicks in the house is the rule here.
Mine are on one side of the coop, with a heat lamp till they are old enough to be without the heat.