Plenty of water and if you work out side consider oral hydration salts in the up coming months. During the summer I take on about 8-10 Lts per day and even that is not enough at times, but I work out side, 10 hours per day
Try drinking as much water as you can in the mornings, so your body/brain doesn't fry during the day. Then water in the afternoon and evenings so that it's a top up, rather than a remedy.
If you are finding it difficult to chug down all the water - especially with proper body salts - throw in a touch of sugar, or one of those little lime/orange powder packets. (Gatorade is the best but way too much sugar. At the very least you will get the body salts.)
But everyone here is right. The more water the better. The AC will definitely dry you out, especially if you like it cold as your body has to work harder to stay warm (as well as cool, during the day).
If you've only been here a few days, you may well still be recovering from the trip. Planes are notorious for their dry air. My parents took a couple days to recover when they came to visit, and after their flights home, my mom actually developed a kidney infection from the dehydration due to flight delays and circumstances that kept her from drinking enough water.
Like hubblybubbly said, try to do most of your hydrating early. Drinking a lot (and I mean water) in the evening will just have you waking at night.
Oral rehydration salts are easy to get and inexpensive at the pharmacy.
Check your caffeine consumption, as coffee and tea can be dehydrating. Stay away from alcohol until you are feeling adjusted. Cold medicines can dry you out, too.
It does take a little time for the body to adjust, so be patient with yourself.
A doc I see here in Dubai for a seemingly unrelated health issue stated unequivocally that dehydration is a contributing factor to a lot of health issues here. And once it heats up and you find yourself going in and out, out into the heat and humidity and back inside into aircon, it can be easy to forget that just because you're not running with sweat doesn't mean you aren't drying out. Aircon is sneaky. And everything in your body needs water--your brain, your joints, your skin, your digestion.
Start your day with a good helping of water. I carry an insulated bottle with me almost everywhere, year round, and my kids do the same.