Instinctively the ideal solution would be to leave your bags at the bus terminal and then go back into town but the bus terminal is almost 40 minutes from the airport and then another 30 minutes back into town so you are already eating into your time in the city.

I cannot see that CTG has a left luggage service but it may well have. That's also not perfect because you are still wasting time. Ideally you'd find somewhere in the city where you could leave your luggage and stroll around from there. When are you going?

Once in the walled city you do not really need a plan, you can just walk around, take in the sites and have a lemonade. It's so hot there that you don't really need a plan. The ambience and architecture are sufficient entertainment