BattleDromes are where the players of Chaotic battle.
The show has only referred to five of the BattleDromes. There are at least seven in all. Each Drome has a CodeMaster and is named after their respective CodeMaster (excluding the BetaDrome which either has no CodeMaster, or the CodeMaster is never there).
The betadrome seems to be the training area in Chaotic. In the betadromes you can apparently make up or negate rules, such as in Dual Duel when Tom and Kaz used Chaor and Maxxor together despite them both being prohibited from entering mixed armies.