[CivicBlues]

I've been to all 3 recently but in separate trips. You could easily do all 3 in 2 weeks with time leftover to do daytrips,
4-5 days in Istanbul
4-5 days in Budapest
2-3 days in Dubrovnik

You can do Budapest-Istanbul-Dubrovnik. As there are no direct flights from Dubrovnik to Budapest.

Alot of this you can find on Google, but here's what I did anyways.

Istanbul: Aya Sofia, Blue Mosque, Grand Bazaar, Topkopi Palace, Chora Church (for the mosaics), Boat on the Bosphorus, Istiklal Avenue, Taksim Square, go to a Hammam. Daytrips: You can go to Safranbolu, but I really like Amasra on the Black Sea.

Budapest: Parliament, Budapest Castle, Churches, House of Terror, Take a bath at one of the bathhouses - I went to Széchenyi Baths but I hear Gellert is good too, go to an Opera- it's super cheap I saw Don Giovanni for 2 bucks. Daytrips: I didn't really go on any, but I'm sure there's plenty of Hungary you can visit.

Dubrovnik: Old City, walk along the City Walls, go to the beaches nearby, take a Game of Thrones Tour. Daytrips: I went to Montenegro for 2 nights (which was great), but you can also Mostar. Both are a couple hours drive away.

Let me know if you need more details for anything.