Another destination before Best of Turkey starts?

Another place you might consider is Malta. It's full of history, although be prepared to be hot, hot, hot due to southern latitude. I flew there through IST either via Turkish Air or Malta Air. Your ideas sound great, by the way (I'd probably pick Tbilisi although Israel would be fascinating too).

I suggest looking at the Wikipedia page of the Istanbul airport or flightsfrom.com to see which cities have non-stop service to and from Istanbul. If you have only a few days, I assume you won't want to spend a large chunk of time getting from your initial stop to Istanbul, as might be the case if you need to take connecting flights. In addition, unless money is no object, you will probably want to look at airfares from your home airport into the initial destination and back from Istanbul (or wherever the tour ends in Turkey). I suspect heading first to a place like Tbilisi may significantly increase the airfare.

Have you considered any places within Turkey? I’ve always wanted to visit Trabzon based on the beautiful photos that I’ve seen of the area, I haven’t been there though.

If you fly Turkish Air (I recommend it), you can get a R/T ticket to any city they fly to, but use the multiple city option. Last summer, I went to the U.S. from Tel Aviv, the price was the same R/T with or without a 5-day stop in Istanbul, though prices were significantly higher for the transatlantic leg from the last weekend in June. So check prices for starting in Istanbul and tacking on days after the tour. It may save you $$$.

What about spending your time in Jerusalem instead of Tel Aviv? The airport is nearly equidistant between the two, and there's tons of history in J-m. Tel Aviv is mostly beaches, museums and modern city, though there are a lot of Bauhaus buildings.

I went on the Best of Turkey Tour this past October and one of my tour mates told me he was planning to go to Georgia. Also, I think Trabzon, as someone else mentioned, would be interesting, there’s a Monastery there - Sumela which looks amazing from the pictures. I have an Eyewitness Travel guidebook on Turkey which gives much detail on other parts of Turkey than Rick’s Guidebook which only covers Istanbul.
Eyewitness says there are direct flights from Istanbul to this part of the Black Sea. Car rental might be the best way to see the sights and most beautiful scenery off the beaten path.

Another voice to the suggestion to include Tel Aviv/Jerusalem: Three years ago I went on a small group tour (not RS) to Turkey. I discovered when booking that if I bought a Turkish Airlines round trip ticket between the US east coast and Tel Aviv (Ben Gurion airport), connecting each way in Istanbul, it was $400 LESS than just a round-trip ticket between the US east coast and Istanbul. The booking rules allowed me to do a 12-day layover in Istanbul on my return from Tel Aviv. Since (as we say where I come from) "my momma didn't raise no fool," I scheduled a week in Israel on my way to Turkey. (I recall the Istanbul-Tel Aviv flight being well under 2 hours.) Thank you, Turkish Airlines! I don't know if tickets are still pricing that way, but might not hurt to check...!

Yep, just under 2 hours flying time and no time change either :-)

FWIW, there's not much to see in Larnaca. My understanding is that Cyrpus is worth exploring by car. Ditto Bucharest vis-a-vis Romania. Tbilisi is interesting, worth maybe 3 days. Getting to the beautiful scenery requires hiring a car and driver. Having been on a bus tour in Georgia, I would not recommend driving solo - drivers are crazy, roads are bad, no one speaks English and signage is in a different alphabet.

For history, though, none comes near to Jerusalem. Or for cultural/religious/ethnic diversity. For something different, add on a day trip to the Dead Sea.

Thank you all for your answers. I realized after reading your suggestions that Israel will require at least week. And since Turkey will be loaded with history too I need a place where I don’t feel overwhelmed and can kind of relax. For that reason I have decided to go to Bucharest. I think the architecture will be fascinating and it isn’t a city where I will feel the need to do ten things in two days. Plus it is cheap and there are direct flights to Istanbul. Thank you again for all of your input!