Which trees are the least vulnerable to fire? These trees will be the "restaurants" (more like small food kitchens) in this mostly realistic world. There will be vents up at the top of the trees for smoke to exhaust.
Ironically, it is generally considered that conifers like pine and cypress are the worst trees in fires; their fibrous bark, year long leaf litter, and oily leaves make them very flammable.
In general the deciduous trees seen in gallery forests in grasslands have good fire resistance. Examples would be oaks, willows, and maples.
My vote goes to the Giant Sequoia (sequoiadendron giganteum), which has fire-resistant bark that can be up to 2 ft/65 cm thick: https://news.nationalgeographic.com/news/2013/08/130826-giant-sequoias-yosemite-rim-fire-forestry-science/ It grows in the Sierra Nevada, an area which is prone to forest fires, and trees likely wouldn't live to reach great age & size without being adapted to fires.
But there's a caveat for the story purposes. It's the bark that's fire resistant, not so much the actual wood (or the needles), so running chimneys up the trees may not work that well.