Inexpensive, beautiful and full of the good stuff; Budapest, Hungary is one of my favorite cities is the world. It is so far off the radar for most American travelers which is all the reason you should go.
They have great fashion and food. The Danube river and all the historic decorative buildings make it romantic plus with the exchange rate, you and your honey can afford to live like royalty.
You can spend the day in castles and the nights under the stars in bubbling hot pools.
Eat what you want and do what you want. We certainly did.