Seeking Home Base Suggestions in North Central Germany

I've stayed in Schwerin, Quedlinburg and Erfurt. I also took a day-trip to Eisenach. I was using public transportation, so from the convenience-by-car standpoint I can only recommend using ViaMichelin.com for driving times, and then padding them.

Quedlinburg has the most historic buildings of the places I visited. As of 2015 the tourist office rented an audioguide, which I used. Even though I had already visited the castle and the cathedral (don't skip the treasury, and Google it before your trip), using the audioguide took me many hours, and it didn't cover every street in the historic area. I ran out of time and didn't get to visit the modern-art gallery. Quedlinburg is a really lovely place, but it gets a lot of visitors, so the main square will definitely be touristy. I'd happily return for the eye candy. The historic center is heavily cobbled and not a pleasant area to traverse with a rolling bag, so I suggest paying attention to where you can park near your hotel. I stayed a the Best Western Schlossmuehle, and I'm pretty sure it had a parking lot. I was booking very late and caught a good deal; I have no idea how its regular rates compare to comparable places; it's well above the quality of hotel I usually seek out. And it is air-conditioned, something you might need if this is a summer trip. I'd describe the location as just beyond the edge of the historic district; it's definitely not in the center of the tourist zone.

Erfurt is a lively, handsome university town with a substantial historic district, a couple of important churches and a merchant's bridge. I guess if you hit it mid-summer there won't be so many students around, but it's a good-sized place and it shouldn't be boring in the evening.

Schwerin has a smallish historic area and a lovely castle/palace in the (artificial) lake. Very pleasant town, but there might be other places that would be more interesting for a multi-night stay. I found a lot more to see in Quedlinburg. I should mention that after a couple of weeks or more of really hot summer weather elsewhere in Germany, I hit cool, damp weather in Schwerin. I guess it's close enough to the Baltic you can run into that even if Berlin is baking.

I didn't have as much time as I would have liked in Eisenach, and there was road construction (or water/sewer-line repair?) going on in part of the historic area, which slowed down my progress. I assume that is long since finished. The city didn't have the liveliness of Erfurt, but the historic area is very pretty.

That's relatively simple:

Thuringia
stay in Erfurt, the capital of Thuringia, which has one of the largest preserved town centres of the country. From there you can do day trips to the most popular places, Weimar and Eisenach with the Wartburg. Other places I like a lot are Schmalkalden (cute little town with timberframed houses and a castle), Mühlhausen (historic town (Thomas Müntzer) with big, historic centre in a rural region) and nearby Bad Langensalza (another cute little town), and Gotha (huge castle with interesting museums).
If you are interested in Christmas stuff: the Christmas baubles were invented in Lauscha, a village deep in the mountains.

Harz mountains
stay in Quedlinburg or Wernigerode. I prefer Quedlinburg, which has a much bigger centre, which I also found more interesting. The three towns you should definitely see are Quedlinburg, Goslar and Wernigerode. Plus cute little Stolberg since you travel by car. Definitely see the cathedral of Halberstadt, one of Germanys most beautiful Gothic churches. Halberstadt itself was leveled in WW2, just like Hildesheim, which offers some of Germanys most valuable Romanesque churches.
Definitely take the steam train up to Northern Germanys highest mountain, the Brocken. If you are interested in steam trains: the Harz Narrow Gauge Railways operate Europes biggest steam train network.

Baltic Coast
Most non-Germans don't know this, but the Baltic Coast is Germanys most popular holiday region, and not just because of the beaches. Four towns, Lübeck, Wismar, Stralsund and Greifswald, are World Heritage Sites, the seaside resorts are famous for their 19th century resort architecture, the islands, especially Rügen, are very beautiful, there are some Nazi relicts (Prora and Peenemünde) etc..
I would recommend to stay not in Schwerin but closer to the coast, and to see Schwerin on a day trip. Rostock is centrally located, but I would prefer a smaller place nearby. Maybe Warnemünde, which is a picturesque seaside resort to the north of Rostock. Warnemünde however is a very busy cruise port, and in case you don't like crowds you could also stay in one of the seaside resorts to the east and west of Rostock. It also depends a bit on your interests. If you are mainly interested in historic places the area around Rostock is a good base, but if you prefer a mix of history and nature I would recommend Stralsund instead, which is a good base to explore Rügen, Hiddensee (a car-free island), th Darss peninsula and Usedom island.

I can't provide info on which town in which to stay. We spend 2 nights in Goslar and loved it. We toured the Rammelsberg Mine which is within walking distance from the center of town. During the tour, we actually entered the mine and went down many flights of steps to get to the mining areas. it was so interesting. You may want to consider it as something different to see and do.
https://www.rammelsberg.de/en/

We stayed in Erfurt on a driving trip primarily because of its location, but thought it was fantastic. Quite a happy surprise. With the car, we stayed at the Mercure Altstadt and it was very good. They had a huge breakfast.

I see Baltic Germany as a different destination from Bach, Luther, or the former East. Would you care for Weimar? Erfurt is a great visit but Weimar has more local sights and more hotel and parking choice. Leipzig is too far East but a nice visit. I still need to visit the Schloss in Gotha. I liked Schwerin but it does not represent the real coastal port cities.

https://community.ricksteves.com/travel-forum/trip-reports/baltic-germany-fachwerke-landesgartenschau

If you plan to stay 3-4 nights in each location traveling in various cities in eastern and Norh Germany, you really do not need a home base,.

I spend 2-4 nights in each place visiting various towns/cities in the part of Germany....Weimar, Leipzig, Halle, Kiel, Eutin/Holstein, Schleswig, Minden an der Weser, Schwerin, Meissen, Lüneburg, Hamburg, Pinneberg, Magdeburg, Lutherstadt Wittenberg, but it also depends on what you want to see.