Big cathedral, small beers
In early March, in fact, it's surprisingly cold, but beggars can't be choosers - we're here because it is so far off-season.
At this time of year, the cheap flights between Prague and Cologne are staggeringly cheap, and we can even afford a four-star hotel.
Germanwings, the low-cost airline operating between Prague and Cologne-Bonn, is very much like its British counterparts, except that the seats are a bit comfier and - amazingly - there's some legroom.
(Belying stereotypes of German efficiency, though, we take off late.)
Our hotel, meanwhile, the Crowne Plaza, is pleasingly soulless and incredibly central. We even have a view of the cathedral.
The last time I was in a four-star hotel I was one of the staff, so staying here as a guest feels like gate-crashing some luxurious but slightly seedy private members' club.
We resist the attractions of escort services and pay-channel porn, though, and set out to see the city.
By German standards, Cologne is very relaxed - people actually jaywalk at pedestrian crossings here, and when we run short of euros at a bar one time, the waiter - unfazed - just tells us to pay what we can.
Cologne's fairly cosmopolitan too. There's a big gay population, and a big Turkish community, which, for our purposes, means great shopping and cheap falafel.
Most obviously, though, Cologne is a city with an enormous cathedral - towering above the city like one of Terry Gilliam's more far-fetched creations, the Dom is simply huge.
Even Prague's St. Vitus, a cathedral of considerable size, would look puny in comparison.
To add to the general feeling of shock and awe, the cathedral also contains the remains of the three wise men, though it's unclear whether one them really is on a scooter, pipping his hooter as the song suggests.
Between the cathedral and the Rhine lies the Old Town, a series of squares and alleyways, dotted with pubs and brewhouses.
Another of Cologne's claims to fame is its beer, Kölsch - which is also the name of the local dialect. (In one of those wacky gags that gets less funny every time you hear it, the tourist guides all refer to Kölsch as "the only language you can drink.")
Oddly, Cologne pubs almost all serve Kölsch in 0.2-liter glasses. (If you ask for a large one, you can sometimes get a 0.3.)
It takes some getting used to, and you see why beer drinkers from elsewhere in Germany regard Kölsch as slightly effeminate, but it does mean that the beer is always cold and fresh.
(In shops, Kölsch is sold in standard 0.5-liter bottles, which must seem like a party pack to the average Cologne drinker.)
The small servings also mean that you can run up an impressively enormous bar tab - marked by the waiter on your beer mat - and still walk away relatively unscathed.
In the culture department, Cologne has a world-class pop-art exhibit, taking up most of the basement level of the excellent (and exhausting) Museum Ludwig's modern and contemporary art collection.
Warhol's here, with his Brillo boxes and his Elvises and his Jackies, along with Lichtenstein and Johns and Rauschenberg and pretty much all the genre's other big names.
Away from the pop-art, our favorite piece was Playhouse, an installation by Canadian artist Janet Cardiff.
Without giving too much away, the work involves a pair of headphones and a curtained-off booth, and feels a lot like something from the movie The Game.
The other standout, upstairs at the Ludwig, is one of French artist Yves Klein's International Klein Blue paintings.
It's simply a canvas painted blue, but the magic lies in the paint itself - an ultra-vivid shade of blue that Klein devised and actually patented.
IKB is almost painfully blue, and has to be seen to be believed. (The postcards they sell in the museum shop don't really do it justice.)
Wikitravel's Cologne page lists the synagogue as another of Cologne's main sights - "notable for its architecture that looks, well, right out of Gotham City."
Clearly, though, it's not on everybody's must-see list, because as we approach the building, an alarmed security guard dashes across the street to check that we're not bent on some sort of hate crime.
A little startled, we leave the area and go shopping instead.
Shopping in Cologne, generally, is an exciting experience, especially compared to Prague.
I barely have time to scratch the surface at Saturn, an enormous record store that claims to have the world's largest CD collection, and there are great specialist bookshops dotted around the city.
Cologne is also the home of Taschen, possibly the world's coolest publishing house.
A small but well-stocked Taschen shop in the city center offers a hefty cross-section of their catalogue, ranging from mass-market reproductions of famous paintings to beautiful design books to arty smut to insanely weighty limited editions on whatever seems to capture Benedikt Taschen's imagination.
(I'm particularly taken with GOAT, a 792-page XXL-format tribute to Muhammad Ali - a bargain at 3,000 euros.)
As you might have guessed, Cologne is also where the original "eau de cologne", 4711, was first produced.
(Cologne is the French name for the city; the Germans actually call it Köln while in Kölsch, it's Kölle. And in Czech, it's Kolín, but there's also a Czech town called Kolín. Confused yet?)
It's Sunday when we visit 4711, so like everything else in Germany, the shop and museum are closed, but we hang around outside in the cold waiting for an automated glockenspiel show to begin, on the hour.
The show, inevitably, is a little lame, but these are the kinds of things you're supposed to do when you're a tourist.
To complete the tourist experience, we also get horribly confused by the public transport system and end up riding the tram towards the airport without tickets, praying that we won't be fined and miss our plane.
Luckily, we don't - our flight home is late too anyway.
Within a couple of hours we're back in Prague, sneering at tourists who can't operate the ticket machines, and struggling to finish half-liter glasses of beer.
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