i found istanbul to be an awesome place, and it has a lot of european relics that can be felt/seen to this day. There is a huge freedom in the city, and relatively speaking, it is extremely cheap. I can't begin to list off the things to do, but if you're interested in knowing more then let me know.
Budapest was neat but less so than Istanbul. It's relatively inexpensive but they nickel and dime you for most things. The public transit is great - almost always reliable and available in like 5 minute intervals, takes you to everywhere you can go. Aquincum(!), SzentLukascs Baths, Memento Park, Vaci utca, Central Market Hall and generally all of District V are great. Take walks along the danube too.
I was only in Vienna for a day but it blew me away. Spend time at Stehpensplatz, visit the rathaus and museum quarter, take a trek to the schonbrunn palace, all are wonderful places. I will spend more time there in the future and unfortunately can't recommend much more.
Bratislava was... Bratislava. No need to go there