The last time we were in Heidelberg and Köln was 35 years ago. Magdeburg was a new city for us.
Heidelberg has grown, added lots of new buildings, a very long pedestrian mall with shops, and a lovely walkway along the river. We walked across to the University botanic garden, which was deserted and a good respite from the Markets; walked up to the Handschuhscheim Market, which took about an hour; walked up to the Castle; watched the river cruisers walk around following the nice ladies with their flags; and had another great gluten-free pizza at a small restaurant (Pasta Bar) off the main street.
The most fun we had was going in to the City Museum, which was open but completely empty. Outside, there were thousands of people in the street going through the series of Markets. Inside, only us and a security guard who followed us throughout the entire museum. How did we know this, you ask? His shoes squeaked quite loudly. We spent two hours giggling while he crept along behind us. We are shady characters. It is a great museum, btw.
Magdeburg was a new city for us. It rained one morning, but was about 10C/50F most of the time, so gorgeous and unusual. People were swinging on the huge hammock under the bridge. There were various markets all over town: one on the bridge; one across from the train station; a large one downtown; and a medieval market where you could throw axes at a target (the line for this was very long, so we just watched). This is a university town, so lots of young people made it lively.
We stayed at the ArtHotel. It was a bit dusty and cold. Go there to look at this HundertWasser architectural gem, and visit the museum, but we would suggest choosing another hotel for staying. The breakfast was very nice. The offseason requires German language skills. The nice young man at the front desk asked me multiple times about the „salon“ as I tried to pay (one must pay for a room when checking in and check-in time is strictly after 1500). We had a (smiling) exchange as I tried to figure out what he was saying about the room, and eventually figured out he was asking how we intended to pay (zahlen) for the room. Neither his first language nor mine was German, so our accents collided for a quite amusing few minutes.
Köln has also grown a bit in the past few decades. The river walk is wonderful. The cherry trees were blooming in December because it was so warm. Definitely unusual, or perhaps usual now! There were many markets all over town, and we walked to each one. My favorite market was across from the building with the giant ice cream cone on top (also the building with both the bookstore and the Lindt chocolate shop on the first floor).
Thousands of local people, lots of river cruisers, many tourists: we were all there! The only thing that has not changed is the Dom, although it was (and probably still is) undergoing renovation and repair. It is still awesome. There is also a Market right outside.
We spent a bit of time in a sidewalk cafe with hot chocolates and coffee watching the shoppers go past. It was a nice final day before we left for home.