A question: Was there a reason you wanted to live in Corpus Cristi? Two bedroom (I am guessing you want furnished) are not abundant, lots more one and three bedrooms. My guess on prices in that area might be from a low of $650 a month to perhaps $1,200 dollars monthly. If you're lucky, I'd consider a fair price for a decently furnished place around $700 to $800 again dollars.
Electric rates are based upon previous consumption. Ask to see previous electric bills to get an idea. Older construction using solid cement makes for living in an oven. Newer construction using more modern insulation materials would provide comfort and cut bills in half. There are a dozen other factors from shade to ventilation and orientation to the afternoon sun that affect comfort and electric consumption. Some claim that people "adjust" to the heat, my personal experience is the opposite. When you're sweating bullets sitting in front of a fan at midnight, that's hot.
Most people "get by" during the daytime and depend upon air conditioning for only a bedroom at night to sleep. With decent ventilation and fans and plenty of hydration, most can survive the daytime heat, even in the summer. You don't want to try to walk anywhere during the "heat of the day" which can start as early as 9:30AM. It isn't just the temperature, but the high humidity that makes the heat so oppressive.
Biggest source of potentially reducible electric consumption would be electric hot water heaters. Turn them on during the cooler months only when hot water will be needed. Forget washing clothes or dishes with hot water or heat a pot on the stove. Test your meter before you move in. Turn everything off, unplug the fridge etc. and then check for any change in your meter overnight. Learn to read you meter and track your consumption. It really isn't a big deal, but rates are higher than what most people are accustomed to and perhaps people exaggerate to prevent sticker shock. Personally I'd consider bills of $150 to $200 a month, paid every two months to be about average for the gringo transplant. Some might sing that their rates are never above $30. After you "learn the ropes" it might well be realistic to have bills in the $50-$75 a month range. Again all amounts are in dollars. There is a significant learning curve and period of adjustment. Some adapt easily, while others struggle to try to adapt the culture and environment to fit themselves.
Paying utility bills will be easy, you can pay at grocery stores, banks or go to the source. Personally I like to pay water bills ahead and go to the CAPA office on avenue 15, between Juarez and calle 1.
The tricky part can come in contracting services for cable TV and Internet. That can be easy, next day set up, or if your area is "saturated" with no lines available....who knows? I have always had good luck and found quality technicians and my cable/Internet installations have gone well.
Now if you have a pool, all bets are off regarding prices.