I train at EpicMMA and can highly recommend it there. It seems to tick all the boxes you are looking for..
It is pretty much on the nose from a budget perspective (I pay 2k per month)
Located at the top of Pedder St, opposite the bottom of Wyndham st in Central
They have plenty of cardio equipment + a comprehensive weight room which few people use
Included in the subscription you have access to as many classes as you want including Thai Boxing, Cross Fit, Ju Jitsu, Strength & Movement + Yoga
They are about to open a facility (Performance Center) dedicated to PT sessions just next door to the main gym for anyone that opts for PT
I have observed their PTs to be of high quality. They appear to be invested in their clients progress and work them hard, taking notes of performance during each session - a small but significant characteristic of a decent PT.
Right now they are having a sale on PT sessions to mark the opening of their new Performance Center with sessions costing between $600-$650 depending on how many you sign up for.
Personally I signed up purely to use the weights as I can't bear the hanging around I have experienced previously in gyms like Pure or FF. I need to burn some of the belly fat so I'll be joining the Muay Thai cardio classes soon to trim down. The classes all seem to be friendly and there is a good community vibe about the place which makes going less of a chore.
My only real criticism would be the locker room which is pretty small and can get crowded if a bunch of classes are all starting/ending at the same time.