Mind Flayers work best as "alien" type encounters....both aliens in general, and the Alien movies. Go with living rooms/areas, and goo, and slime, and muck and eyeballs and tentacles.
Giving them weird psionic powers works out too....or if you need to just make them illusionists, and call it 'mental powers/psionics'. They work get with illusions that make you think the pool of acid is a pool of water and that sort of thing.
You really want to "go up past 11"....so it's not just a dark cave made out of living flesh....it's a cave with hungry living darkness that bleeds 'light' blood
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By the books the Underdark only messes with conjurations and divinations....mostly teleport and scrying. Anything else is left open.
I like all sorts of strange magic in my Underdark, tunnels that move for example, but I have that stuff on the surface too..