So, you can spend two weeks in the area. In this case you could consider three bases to see Saxony too, or explore "Luther land" in-depth since you can get to places which are difficult to reach by train. And by car the Harz mountains are doable day trips both from Leipzig or Erfurt btw.. If you do mostly day trips by car I wouldn't want to stay in Leipzig however, since it takes some time to get out of the city. Erfurt is smaller and, according to Rick Seves, a "untouristy Rothenburg", while nearby Weimar is a very pleasant small town surrounded by castles and parks. Both great bases in my opinion, but getting to Wittenberg will take some time (on one of Germanys busiest Autobahns).
If you want to explore "Luther land" more in-depth: this isn't only Luther's land, but also Bach's land, and in the past this region was separated into many tiny duchies, among them Saxe-Coburg-Gotha, where the Windsors are from. Every tiny duchy had a tiny capital, and every tiny capital had a huge castle. The most interesting are Gotha and Rudolstadt, with really absurdly big castles. Other former capitals with such castles are Schmalkalden, Altenburg and Coburg. Other places I like are Bad Langensalza, the Saalfeld Fairy Grottoes and Lauscha deep in the mountains of the Thuringians Forest, the place where the Christmas baubles were invented.
The Saale valley is something like the Rhine of Central Germany, with quite a few castles and a wine growing-region around Freyburg, near Naumburg. Freyburg has a impressive castle btw.
I don't know if I would recommend a full week in the Harz mountains. After a while all these preserved towns full of half-timbered houses look a bit similar. To me Quedlinburg, Goslar, Wernigerode and Stolberg (a hidden gem where a car is needed) are more than enough, but with a bit of hiking, the steam trains, the cathedral of Halberstadt and one or two Romanesque churches (some of the best in the country, and World Heritage Sites) it's of course no problem to spend a week, or more, there.