suggestions for two days in Weimar

I have been waiting to see what answers you might receive. I am thinking of visiting the Erfurt/Weimar area next spring. They appear very close to one another, only about 15 minutes by train. Michelin Green Guide gives Weimar 2 stars and Erfurt one star, listing quite a few things to do in each. For me it is a good source if you do not receive personal input here.

I stayed in Erfurt in 2015. It has a beautiful historic center that I believe did not sustain much war-time damage: two historic churches, a merchants' bridge, and interesting early 20th century architecture as well as much older stuff. It's a lively university town. There's also a Martin Luther connection, so possibly some related sights. Erfurt was covered in one of Rick's fairly recent Germany videos, available to watch on this website.

Outside Weimar itself is the Buchenwald concentration camp, which was also used after the war to house enemies of the state. There's good English-language explanatory material about both periods, so allow adequate time to peruse it. There is bus service from downtown Weimar, but it's a bit of a ride out to the camp and the bus may run only about once an hour. Not sure about weekend service.

Eisenach has a pretty historic center, plus the very impressive Wartburg Castle (access via city bus, but there's still some walking required; not sure about bus frequency). English-language tours are available at the castle; the website may provide info on the times; I had to wait some time for my tour to begin. The castle has a Martin Luther connection.

Well, first of all Weimar is a beautiful town, with a nice, mostly preserved centre surrounded by castles and parks. Even if you don't visit museums it's a very pleasant place just to walk around. Sites in the surroundings are either Belvedere castle or KZ Buchenwald.
Coburg can be done as a day trip, but it takes quite a long time to get there, so I would recommend to focus on Thuringia instead. Bad Langensalza is really off the beaten track; I think even most Germans don't know it. I was there a few years ago. It's a lovely, typical Thuringian town with a nice, small and colorful old town, one or two not so important castles, and even a partly preserved town wall and a Japanese(!) garden... actually, that's just one of several small gardens. But it's a small town that needs only half a day at most. I did Bad Langensalza in combination with Mühlhausen, which is 30min away. Mühlhausen was far more important (a free Imperial city), has a much bigger old town (with a few losses), a better preserved town wall, and more (Gothic) churches... but it's equally unknown.
Eisenach offers a mostly preserved centre without major highlights. The reason to go there is the Wartburg, a World Heritage Site and Germanys most important castle. But it takes some time to get there, and it's not really off the beaten track.
But I still think the best day trip from Weimar is Erfurt, the capital of Thuringia. The city survived WW2 almost without losses and offers one of Germanys biggest preserved old towns today. Rick Steves actually wrote about the city here.

So, I would recommend to start with Erfurt on the first day. If the city takes the whole day fine, if not return to Weimar and stroll through the town for the rest of the day. On the second day either see Weimar and maybe a second place nearby(1), or, if you think you have seen everything of Weimar on day one, do a day trip(2).

(1) this could be Weimar + Bad Langensalza or, if you are looking for a preserved town with a bigger highlight, Naumburg. Naumburg is just 30min away and offers a nice old town plus a famous cathedral.
(2) this could be Bad Langensalza + Mühlhausen, or Eisenach + Wartburg castle, or maybe Leipzig, if you want to see a big city.