Good view from the hotel
We had selected the City Hotel from an online guide, asking the Allee Hotel in Neustadt to make the reservation for us. We probably should have drawn some conclusions from the great difficulty the clerk reported in making the reservations over the phone but after she had worked so hard we didn't want to interfere.
In Heilbronn we ate lunch at the train station -- two sandwiches, a shared pastry -- because we have learned that on the weekend everything is closed. Then we set out to find our hotel. The picture in the guide showed the hotel sign high on a building; it occupied two high floors of what was described as a shopping center. Sure enough we found the shopping center. It seemed to be a collection of offices surrounding a vast empty lobby, with a sign directing us to a side door to enter the City Hotel. The door was locked. Outside the door was a sign that said on the weekend to get into the hotel we needed to call a number. A long German phone number. We could see into the building where the elevators were, but the door was locked. It was cold with a light mist, threatening to rain harder.
But we carried no phone and there was no phone at this door. Just as we were beginning to worry a lot we were saved by a woman leaving the building, who spoke some English. She helped us brace the door open and went the extra mile by phoning that long number. Eventually she was directed to go to a particular mailbox just nearby, reach inside and pull out a chain, use the key on the chain to unlock a separate mailbox where there was an envelope for us (with our name on it), with building key and room key and room number!
So there we were in this building which now appeared to be entirely empty except for us. Up we went to the 14th floor, City Hotel, where we found the Reception area (unstaffed). Re-reading the envelope we saw we were to go to the 12th floor, which we did, and found our room.
It was a pretty basic hotel room. We set up our computer and needed of course username and password. We found a button marked Rezeption on the desk phone and pushed it and in the fullness of time (the clerk was the owner and had the phone call forwarded to her home, which was another apartment in the building) we were told the password which involves "what is the mark over the number one on the keyboard" (hint: exclamation point).
Good view from the hotel
So we had the room and the Internet but we knew we needed something to eat before Monday morning so, with Bob carrying the keys very safely in his pocket, we went out into the city, where it was getting colder and colder and starting to sprinkle. After making several tries at side streets with closed stores we picked up some McDonalds' food and returned to the hotel, where the keys worked as advertised.
So then we had Internet, food, Kindle for reading, some tourist info in German, and a tv which shows, in addition to the usual, CNN and BBC World News in English. We settled in as it got colder and grayer.
But we began to notice that the room was not warm. It was, in fact, quite cold. Had they turned off the heat for the season? Had they forgotten us? Were we supposed to find the switch? Again,we pushed the Rezeption button. "Mein zimmer ist kalt." we told the woman who answered. There followed a long discussion between the people in the room where the phone was answered. Then the phone went to busy signal.
We pushed the button again. This time I got a promise that somebody would come over. And in about a half hour a very pleasant young lady (the owner) appeared and patted the cover of the radiator. Then she turned a couple of dials. "Broken," she said. "Mein Mann kommt."
Sure enough in about ten minutes a young man (the owner) came in bearing two handfuls of tools including a new part for the radiator. In moments he had replaced whatever he was to replace. We all smiled.
Then he said something about morning and we said Seven O'Clock, we all shook hands and he left. We figured out he didn't look so happy because it was the weekend and breakfast was so early. Also very few people stay over the weekend, so he had rather been 
The Fishing Bunny
hoping we would say Nine O'Clock so he could sleep in, but no luck. We weren't going out drinking and dancing so we wanted breakfast early!
So we had the room, the keys, the Internet, the rest of the McDonald's food, the Kindle which we are sharing, some peanuts and chocolate we brought from the Hotel Allee, and the room was slowly getting warm. Also, we had a very good view out of our 12th floor window!
At seven o'clock Sunday morning there was breakfast for us, quite good.
In the following days, we toured Heilbronn and also used Heilbronn as our departure point for trips to nearby cities. We learned to find our way to grocery stores and eating places, and we appreciated some of the city features, notably the Fishing Bunny which was not, as we had suspected, a left-over Easter decoration but a work by a local sculptor which is on permanent display. We liked the play toys for little children which were built into parks and streets in the pedestrian area. The city as a whole failed to excite us, but near our last day we learned that our hosts, Svetlana and Ivan, are Russian and fairly new to the hotel industry, still learning German and working hard to make a go of their enterprise. This warmed our hearts somewhat.