What kind of weather are you looking for? Southern Spain and Portugal you'll still get some decent sunshine in October. It'll be Autumn elsewhere and Scandanavia will be distinctly chilly. I've been to Stockholm in October - beautiful city but you'll need warmer clothes than the UK!
Suggested Tavira above as you'll have nice sunny weather - would second Seville and Granada. Prague won't be warm but is probably the most visually beautiful city in Europe and would be nice for an anniversary weekend and very do-able in 2 nights. Cologne makes for a nice short break and is easy to get to, easy to get around it's charming old town. Nice is beautiful now they've spent a fortune on it & again easy to get to and easy to get around - it's probably worth a longer break though as there's much in the area to explore within easy train reach.
Carcasonne with it's medieval hilltop fortress is about right for 2 nights, its very pretty, got lots of history and easy to take in. There are direct short flights from London (alhough unfortunately Ryan Air!). If you don't fancy flying, Bruges from London is easy and quick to get to by train, compact and the food and beer are good!
The better known Italian cities will be less rammed in October and most make for a great weekend break. The obvious are Rome, Florence and Venice - they'll still be busy but not as unpleasant as in the summer and you'll have a bit better weather than here. Bologna is a pretty, less visited city (and would second a trip to Modena which is easily reachable by train) with direct flights from the UK. Verona (has it's own airport) with is a romantic city with it's links to Romeo and Juliet. The old Roman arena has nightly musical performances which are bookable in advance. A day trip in 2 nights would be pushing it a bit but Venice is just over an hour away by train from Verona or you can take a bus from the station to the towns on Lake Garda and be there within 45-50 minutes.
Ortigia in Siciliy (fly into Catania, take a 30 minute train - longer travel time but worth it) is less well known, has lots of history, won't break the bank and is incredibly pretty and also fits the romance vibe (lots of Italians get married there). It won't break the bank either, a nights stay in a decent hotel will be a lot less than you'll pay elsewhere in Northern mainland Italian cities. In terms of other Italian cities , can't stand Milan, other than the Cathedral and unless you want to go shopping it's pretty ugly and souless (apologies PP, horses, courses and all that!).
Basically, you've a huge amount of choice! All depends on how much you want to spend, the amount of time you want to spend travelling and how much sunshine you want and I'd narrow things down from there. But loads of great, great options!