Engagement trip

[55offsuit]

Me and my girlfriend are planning this trip somewhere in Europe for our engagement. It will be for the weekend at 11-14 october, maybe to 15 october. We have so far looked at Salzburg (kind of out of budget), london, paris, amsterdam and zurich.
We have second doubts about all of these. So was just wondering, where is a good place to take your girlfriend for an engagement trip in Europe? Budget is like 800$ for hotel&flight.

We want it to be romantic and with nice places to enjoy at days, like museums, parks etc.

Thanks