Going to the BAA for high tea is a once in a lifetime thing, and not actually THAT bad value for money. You get a whole meal out of it, which is more than some teas in the world. Sure the decor isn't to my taste, but to gawp at it for an hour or two it's pretty fun. I still get a funny feeling in my tummy when I see the building from the outside too!
Taxis are cheap in Dubai or if you have data then use Careem with discount codes, so don't be put off from staying on the Palm unless you are going to be out all the time.