Istanbul is pretty inexpensive to get to. Is it safe? Don’t know. We were there last June, don’t think I would be as eager to go this June. Loved the architecture and the food, detested the customs and crowds. Certainly glad I went. Great life experience and educational experience. But what we did that was simply amazing was that we flew into Sophia, Bulgaria. This was our second trip to this wonderful country. The first time we saw maybe half the sights and had a terrific time. This time we concentrated on driving cross country for a week, fishing at every river we crossed. Great fishing trip. Our last stop in Bulgaria was Nessebar which is an amazing ancient town with some pretty decent beaches nearby. From Nessebar we drove on to Istanbul. After a few days in Istanbul we flew on to Budapest. Direct flight, about 2.5 hours and under $300.
You didn’t mention budget so here are some numbers. A car with a driver/guide plus hotel rooms will set you back about $300 a day in Bulgaria. A great apartment in Budapest for a week will set you back about $65 a day. Really nice hotel in Istanbul with a roof top terrace / restaurant is about $225 a night.
We use Budapest as a base pretty often (like 2 or 3 times a year). Budapest to Moscow or Jerusalem is about $300 round trip. The high Tatras of Slovakia are just a few hours north (where you will find us fishing in May), Vienna, Salzburg within an easy train trip. But I prefer Pecs in southern Hungary and Eger in the northeast. One for the really unique relics of ottoman and Roman history and the other for the good, inexpensive wine.
If I were going to go to Dubrovnik I would pair it with Montenegro, Albania, Macedonia and maybe Bulgaria if time permitted. It is beginning to look like you will find us fishing in Macedonia in the Fall with the trip beginning in Tirana Albania and ending in Sofia Bulgaria. Great part of the world.
If you haven't been to Istanbul its worth the consideration. But think out of the box and look at where Turkish Air flies direct out of Istanbul. Some place we have on our list are Azerbaijan and Uzbekistan. Both fairly short non stops out of Istanbul and amazing places to visit.
Where ever you go, you make it what it is. So go make it a great trip.