I lived in Turkey when I was working for METU out of Kerkenes....despite what nasty things most folks have ingrained about Middle Eastern countries, this one is gorgeous!
The people are amongst the friendliest I've ever chanced to encounter, the scenery is lovely (moreso on the Western side and near the coastal areas), and there is just so much culture and history that you couldn't hope to see it all in a lifetime.
The best part is, it's incredibly cheap and easy to travel there. You can find a NICE hostel for under $6 a night--dinner and breakfast usually included. Everywhere in that country is linked by their extensive bus routes...equally inexpensive. Turkish food is incredible, and extremely affordable. Very safe, too---I travelled alone for 3 months and was treated like gold everywhere I went, especially in the more rural areas.
The only places you may run into trouble if you're thinking of going are the major cities and tourist areas (most of them are in the West).
I would avoid Izmir altogether.
You won't want to miss Istanbul, but be wary, especially around the crowded old-district which makes an appealing target for monsters looking to stir up chaos against Westerners. If you do head to Istanbul, I recommend a nice hotel just South of Hagia Sofia called "Karasu Green"---it's owned by a Turk who is married to an American woman, and they really go out of their way to see that you have a great time.
Other places not to miss (especially if you're a history buff) are Cannakale (which is where you need to go if you'd like to visit the ruins of Troy. It's also about 20 minutes from Gallipoli, if you're into WWI sites), Ephesus (The old Temple of Artemis was one of the 7 Wonders of the World, but the Great Library is still there--and not to be missed), Goreme (where you can see the breathtaking landscape of Cappadocia, and be exposed to a lot of Early Christian history)----and for craps and giggles (and since it's on the way) stop by Pamukkale and take a dip in the fizzy pools. Head South to the coast and you've got your pick of seaside villages. Over at Olympia you can climb the hills and see awesome natural firelights, and some well preserved ruins.
That's the Western side....if you wanted to go further East, Ankara is a good place to start. Lots of history there, and one of the nicest National museums in the country. From there you can go to the GREAT ruins of the Hittite capital "Bogazkale". I would also recommend day trips out to Chatter (a site about 3 hours South of Ankara), and Kerkenes Dag (About 30 minutes from Sorgun, in Yozgat). The dig teams there live with the common folk in tiny traditional villages...and are always happy to get visitors. They would be likely to throw a feast in your honor if you showed up, and it's a great way to immerse yourself in the culture.
If you were feeling really adventurous, you could go further East to Lake Van, which is beyond beautiful, but it's so close to the Iraq border (and is also deep in Kurd territory) it's honestly not the safest place to visit right now.
Anyway--this is a much longer post than I'd intended--but suffice it to say that Turkey is well worth a visit.