Have been to Istanbul, the Aegean coast, and to Cappadocia, where the fairy caves are. The country is indeed magical, friendly, and very safe. We rented a car and drove all over Cappadocia. Didn't speak any Turkish, but everyone tried to help us find our way (we got lost several times.) Frankly, I think it would take several weeks to do the country justice -- it's very large, with very distinct areas. Do you want to see incredible scenery? Try Cappadocia, where there's weird moonscapes and ancient underground cities that go as deep as seven stories (the locals used to hide underground from the Romans.)
For culture and food and of course nightlife, there's Istanbul. First-timers often stay in the old city (Sultanahmet) because that's where a lot of the tourist sites are. From Sultanahmet you can walk all the way to the Grand Bazaar, see the Blue Mosque, etc. But on your second trip, you might want to stay in the throbbing and fashionable Beyoglu neighborhood where some truly great restaurants are.
The coast is where a lot of archaeological sites are. It was the outer reaches of the Greek empire, so you'll find many unexplored ruins where the only living things are goats wandering around fallen temples and statuary. We even found some ancient coins just lying in the soil. The jumping off point for a lot of Aegean tourists is Bodrum -- a nice seaside city, but often overrun with drunk UK tourists.
Have a great time. And don't mind the pesky carpet sellers. They're just doing their job, and they don't take offense if you tell them to get lost. Once, I told a particularly annoying carpet seller that I'd bought a carpet the day before. He answered: "But today is another day!" You can't help but laugh at their persistence.
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