It's very simple in Broome,
town beach is pretty much the Only main kite spot that works with any winds with an Easterly component in it, E and SE being the most favorable/common directions. It's also where you will find the handful of local kiters. It's very tidal so you have to look out for rocks at lower tides and also the minimal space to setup / launch / land at higher tides with plenty of tourists around.
www.google.com.au/maps/search/town+beach+broome/@-17.9712109,122.231454,1847m/data=!3m1!1e3The winds are typically not very strong, so hopefully you have some light wind setup.
You could kite winds with Westerly components on the other side (Cable Beach) but they are typically light as well. Cable beach is a paradise for land kiting (buggy or mountain board) as the sand is very hard and lots of area to play with.
Have fun
Christian