The WiFi is non-existent. Couldn't connect to it anywhere in the hotel, despite having at least 2 bars most of the time. Even in the breakfast room I had no luck, and I tried a phone, computer and iPad at different locations throughout the hotel. Luckily I had a SIM card which made it a bit more tolerable, but I'd have been super frustrated if that hadn't been the case. Germany is really lacking in free public WiFi hotspots, so a hotel without any is a big issue. Easily fixable, and I hope that happens soon.
Domhotel was quite lovely, great location right near the Schlei waterfront, nice walk to Schloss Gottorf and the old town. I didn't have breakfast so I can't comment on that, but the hotel was very clean and well-maintained. I had room 14, the single room on the top floor, and it was well-sized. The bed was a day-bed, making it bigger than a standard single, so that was a big plus! Having a sink in the room was also great, but it would have been nice to have a plug to do some washing myself.
The shower room was right next to my room and quite loud when in operation, but the guests stuck to the strict 23.00 curfew for showers, which meant my sleep wasn't at all disturbed.