Disclaimer: This post is going to jump into the deep end of nerdom.
The HMS Unknown is home to everyone on the show except for Barry and Marisol. Built in the grand tradition of wooden sailing vessels, the HMS Unknown looks to be a relic but is actually quite futuristic. The ship exists between time and space which allows passengers aboard it to travel to distant planets as well as back and forward through time. It is allowed to do this because it's equipped with twin Paradox Thrusters (see Disclaimer above). I wanted more than to just call it a magical traveling boat for the sake of the emphasis on science in this show. For a young audience, I feel this is a good and whimsical explanation as to why our cast and crew are allowed to travel to all these fanciful places.
The interior of the ship has a Jules Vern-ean / steampunk asthetic. Everything is more grand than it needs to be. Lots of brass knobs and embellishments, darkly stained wood paneling, and bellows that breathe in and out for various pieces of machinery. This is what I imagine the ship's navigational computer to look like:
Much of the show takes place in the ship's galley where the science crew hangs out and Sergio cooks. The galley is furnished with simple tables and benches, decorated with maps and posters of things like the periodic table of elements. The ship also has a laboratory where the crew and Barry run experiments.