Great European cities to visit?!?

For the past couple of years I have been trying to do an annual European vacation. Usually I like to fly to London and team up with a friend who lives there, spend a few days in London and then hit a fun city nearby. So far I have managed both Paris and Barcelona. I am pretty confident in my ability to travel at a wallet friendly rate, but this year I just don't know where to go!!

I want to do a big trip to Italy, so that is out of the question this year. I started looking into Ireland (mainly staying in Dublin with some day trips to other attractions since it's a small country), but it just seems quite expensive and I keep reading that hotel and travel prices there have nearly doubled over the last couple of years.

Basically I am looking for a great city to visit that is in relatively close flying distance to London. I would prefer a place where public transport is readily available and I can stay entertained in that city for 4-5 days easily. I am just not up for planning a trip where i have to travel around the country to multiple cities. That is what made a trip to Paris and Barcelona so easy and accomodating...everything was right there and there was plenty to do!

I was thinking maybe Madrid? Some place warmer is always appealing!! Any suggestions would be greatly welcomed!!

Thank you =)