As Philadelphia, the city was founded in 189 BC by the king of Pergamon. Most of the city is quite new, as the town was burned by the Greek and Turkish forces during the Turkish War of Independence. Today Alaşehir is an agricultural center and market town, rather run-down, with little to see and not much to recommend it. (If you're interested in a traditional market town for Turkish farming country, Akhisar is much nicer.)
By busAlaşehir is easily accessible by bus from Izmir, costing about 20 TL for a one-way ticket and running roughly every two hours. These buses also stop in Manisa, and it's possible there may be more frequent minibuses to be caught in Manisa.
By trainThere are two daily trains (each way) between Basmane station in Izmir and Uşak, and one between Izmir and Konya which stop at Alaşehir. The Alaşehir train station appears to be in the center of the town. There are also daily commuter trains between Alaşehir and Manisa, leaving Alaşehir early in the morning, and returning from Manisa to Alaşehir in the afternoon (making them impractical unless you plan to stay overnight in Alaşehir).
Alaşehir railway stationaddress: Atatürk Blv
Alaşehir is small enough to be easily navigable on foot.
There's a monument in Alaşehir celebrating the liberation of the town in the Turkish War of Independence, which the locals are quite proud of, despite its resemblance to pretty much every other liberation monument in every other Turkish town that played a role in the war. There's also the ruins of the Church of St. John (St. Jean Kilesesi), though it's only open rarely (possibly by appointment), and locals seem uncertain of exactly when the church can be visited. There's also a bit of a ruined wall by the bus station, and a fake castle down the road.
Aside from walking around the town, it's possible to check out the market, and buy fresh produce.
Fresh produce, on market days (of which Saturday is one, though there may be others).
If you're in Alaşehir, it's probably because you want to see the Seven Churches of Asia. Two of these churches are nearby, Sardis in Salihli, and Laodicea, near Denizli. Sardis can be reached by train or bus, while Denizli can only be directly reached by bus or (or possibly minibus) or private transportation.