If you board a Havas bus it will stow your luggage during your transport. If you need to you can keep your luggage at the airport while you make your way to Izmir center. There may be a fee involved? Ask an airport attendant. If you are ultimately going to depart from Izmir airport again, check your luggage into your airline - they will may keep it for you/
Havas buses usually leave about every hour. If you Havas into the city it will leave you at Efes Hotel a 5 min walk from Konak Tower on the seacoast. Izmir is so big - you may want to get online to look for points of interest to cab to.
I suggest walking around the Konak area leisurely and grabbing a nice mean with tea afterward.