One of Turkey's key coastal cities, Izmir is located on the Aegean Sea, a large bay of the Mediterranean that is created by Greece on the west, Turkey on the east, and Crete on the south. Because of its position, Izmir is a key hub of trade between the Mediterranean and the Middle East, and as such is also a melting pot of the 2 cultures, making it a different environment than traditional Turkey and definitely more cosmopolitan than Izmir's neighbors to the east and south. Because of its location on the coast, many of the best day trips out of Izmir are to some of the smaller cities along the coast of the Aegean that offer beautiful scenery and more of a small town feel than the booming metropolis of Izmir. Historical attractions are another good reason to get out of the city, as the entire region is rich in historical sights.
Cesme
About a 30-minute drive from Izmir, Cesme is a popular sea-side town and resort that makes a great get-away from all the activity of Izmir. Attractions here include Cesme Castle, which sits above the town and presents a great photo opportunity, and the beach, which is a great spot for windsurfing and kite-boarding in addition to old-fashioned relaxation. If you don't have a car and don't want to rent one, you can take a bus from Izmir to Cesme. If you are interested in continuing your exploration outside of Izmir, you can hop on the ferry to check out the Greek island of Chios, famous for its beautiful scenery.
SelcukAnother option for a trip outside of the city limits of Izmir is to head to Selcuk, a city that's a little farther away but has some great historical sights. You can take the bus here as well if you don't want to drive, or there is also a train connecting Selcuk with Izmir. There are a number of interesting sights in and around the city, including the remains of The Temple of Artemis, one of the 7 wonders of the ancient world. If you head south of the city you'll find the House of Mary, which is claimed to be the house where the Virgin Mary spent her last days. In downtown Selcuk you will find the Byzantine Citadel, remains of Roman aqueducts and the Museum of Ephesus, which contains artifacts found at the nearby ruins of the ancient city.