Stay in one spot and take day trips or move around every 2-3 days? The Latter is exhausting.

For weather, May will be much better, and the first half of June is very nice and still before the tourist horde descends.

I am a "hub and spoke" traveler myself, loathe the "2 nights and keep moving/packing/unpacking" approach to travel.

Well, April will definitely be colder than May. I usually travel to Europe in early to mid-May, because I find it is warmer but not as crowded as it gets in summer.

With regards to your proposed itinerary, I'm sure many others here will have some ideas, too. But my initial thoughts are that you are somewhat spread out. You could easily do 3 nights in Munich, then take a train to possibly Nuremberg, which would be a good base, and then take day trips (again, using the train) to all the interesting cities and towns nearby, such as Rothenburg o.d.T, Würzburg, Bamberg, and so on. You could even take a day trip to Meiningen, although it's a bit far by train. OR you could base yourself in Würzburg, which is closer to Meiningen but still close to all the other cute towns in Franconia.

Bacharach is farther out and several here will tell you that there are better places to base yourself. But again, if you wanted to go to the Rhine, it's easily doable by train. Or you spend a bit more time where you are and then at the end of your trip, take the train to Berlin for however many days you have left. Will you be doing an open-jaw trip (flying into one city and out the other)?

FWIW, I am heading to German the end of April and will be staying there for a month. You can find my (sort of) itinerary on this post if you want to check it out. https://community.ricksteves.com/travel-forum/germany/should-i-rent-a-car-while-staying-in-the-countryside

There isn't good or correct answer to your question other than. "It depends ....." When we were younger we tend to hit a lot of places because we had the energy and limited time. Your proposed trip is a little strung out -- Berlin to Munich. For day tripping you need to have a location that is surrounded by areas/things you want to see and do. And whether train or car, again, it depends on where you are staying. It an area is well served via train, then a car makes more no sense. But for the general country side, away from major metro areas, then the car may be the only option. We now stay about a week in each location and do some day trips but those trips are limited. You may want to do a combination.

We always debate the "stay in one place with day trips or move around" as well. We don't have tons of vacation time at this point (we are in our early 60s). I always want to see and do as much as possible. My husband is happy in one charming town or city with 1-2 day trips LOL!

So, we compromise. Our new model (except when we are taking our adult kids) is to stay put in one vibrant town, take day trips, even an overnight but not give up our apartment. The town is key because it has to have enough to see with regards to museums, shops, cafe life, churches, history. Then, we end our trip with one place where I can hardcore sightsee if that makes sense. We did this in Aix-en-Provence for 4 weeks, then went to Paris for the weekend (been there a lot so didn't feel the need to stay longer) and then a week in Florence).

We may choose Colmar or Strasbourg next so we can day trip a lot. Then fly home from Brussels or Amsterdam so I can get my "fix". LOL

That said, we are planning a trip for Southern Spain and Portugal and going from Madrid to Sevilla to Lisbon to Porto in two weeks. And for Christmas 2023 with our kids. I think we will focus on Munich, the Bavarian Alps and Vienna.

April is our favorite month in Germany. True, it can rain or snow, but cool and sunny seems more the standard.

We lived in Germany for 6 years and had a car. It is nice in the country but a pain for us in cities. Plus, there are few places more aggravating for me than the autobahn.

We prefer 2-3 days per location and then moving. Our most enjoyable activity is to stroll through a modest sized town in the evening. Two days is usually enough per town. We would not like those prime evening hours to be spent returning to a base. Still everyone is different.

Every time we traveled to Europe we have tried to do too much. It's
exhausting. If it were up to me I would rent a house in one beautiful
place in the country in a small village and take day trips.

This can work and WILL work if you plan thoughtfully. Why not try it? What you need to do is give up the notion you will "see Germany" in 2 weeks. That's impossible anyway. Day trips only work well if you're spending at most 3-3.5 hours in transit on a given day (the point is to get your boots on the ground, right?) So what you'll be doing is exploring smaller areas, or parts of those smaller areas.

I suggest you select 2 separate areas and book a rental for one week in each. My picks, based on your list, are as follows. Look closely through the options and see what interests you in each.

1. Rhineland Palatinate (Bacharach area) For a week you might focus more narrowly on the Rhine (A unesco World Heritage site) and Mosel Valleys.

https://whc.unesco.org/en/list/1066

https://www.rlp-tourismus.com/en/experience/culture/stories/the-romantic-cities-in-rhineland-palatinate

http://www.loreley-info.com/eng/rhein-rhine/walking-hiking.php

https://www.mosel-inside.de/en/travel-guide/mosel-villages.html

https://www.tripadvisor.com/Attractions-g8319518-Activities-a_allAttractions.true-Mosel_Wine_Region_Rhineland_Palatinate.html

2. Franconia (Rothenburg area.)

https://www.frankentourismus.com/cities/

https://www.frankentourismus.com/regions/

Meiningen looks kind of cool to me... maybe worth more than just a drive through, especially if there are familial routes roots there.

https://www.meiningen.de/

I'm a believer in moving around efficiently via car! Your itinerary looks good to me.

Meiningen looks kind of cool to me... maybe worth more than just a drive through

In April, it's still opera season and thus a good opportunity to visit the small but famous opera house (von Bühlow, Reger and R. Strauss directed it, and Brahms' 4th symphony premiered there), which is still amazingly good.

I've found that I prefer something between the extremes of just one base and moving every 2-3 nights. On a typical trip, I mix it up with some longer and shorter stays. For example, for our last three 2-week trips we have done the following numbers of days in various stops. We have only done one night stops when we had a very specific site to see on our way from one place to another (for example: Pompeii and Giverny). This has worked well, giving us a variety of experiences without exhausting us (we were in our 60s for these trips.

1, 4, 2, 8
1, 5, 8
5, 6, 1, 3

I depends on if you can find enough to keep you busy based in one town. I’ve spent a week in Bacharach ( at one time, 20+ days total ), Tuebingen, and Salzburg ( and a week in Callendar, Scotland ) as well as 5 days in other towns. That is my prefered method these days, but 2-3 days in any town also works well.

We travel regularly to Germany to see family. I suggest that you stay a few days in each city and move to the next via train. Most train stations are in the heart of the city for example Cologne, Nuremberg, Munich. There are family train tickets that allow you to travel in one state for around $30 a day for up to 5 people. Travel can begin anytime after 9 am. The DBahn website has information about the tickets. The DBahn website is available in English and easy to use. We have used the IBIS hotels which are very basic but clean and come with breakfast. For a little more comfort consider the Adina apartment hotels. I use the DBahn website to find hotels figuring that they have been vetted. I avoid American chain hotels because I travel to experience something different.

The only thing I would change is to spend 5 nights in Berlin and see Leipzig as a day trip. That would give you enough time to see Berlin plus another day trip somewhere like Potsdam.

How about Erfurt as a base? I like it a lot, and it could potentially trim your stops to Munich - Erfurt - Berlin, a trip I personally would love. Erfurt is popular with German tourists but certainly not overrun. It avoided Allied bombing during the war and has a gorgeous old town. It has many original half-timbered houses set in a living, breathing city (as opposed to a lot of rebuilt houses set in a tourist town). It has an enormous cathedral. It has a very old synagogue (14th century as I recall) that escaped Nazi destruction because it had been turned into a warehouse. It has parks. It has a very relaxed vibe. It was part of East Germany, so it has cold war history. It was the home of Topf und Söhne, an industrial giant that made, among many other products, the ovens for Auschwitz and other concentration/death camps; the now defunct company's main building has been turned into a museum dealing with how seemingly normal owners and employees at a normal company became entangled in state-run genocide. A list of things to do there: https://www.thecrazytourist.com/15-best-things-erfurt-germany.

Meiningen? 1 hr 16 min with 0 stops by regional express train
Leipzig? 40 min by ICE train
Bamberg? 45 min by ICE train
Weimar? 12-15 min by regional train
Rothenburg? Too far away -- not sure how attached you are to this

Recommended lodging: Hotel Domizil just barely off Domplatz. Something like 11 rooms. Run by mother and son. Son is a chef by trade, so breakfast is a true treat. https://hotel-domizil-erfurt.de/en/home.html

We are not hub and spoke people. After all, we are traveling. There are many places to see. We might do one day trip from a certain city, but to stay in one place and go out each day to another place, and return, we do not feel is a good way. Travel time, inability to enjoy the one day place outside the day hours. It is like a cruise ship docking for one day in Venice. Oh gee, we saw Venice.
We do have friends who are spoke and hub. For months at a time. I think they do it for what they think is the “real” experience of that area. Also to save money.
We very rarely go to any destination for one night, though that is much longer than a day trip would be. Day trips are used for say, visiting Pompei, or a tour of a vineyard. A finite experience.
Hub and spoke travel only saves you the time for hotel check in and packing. There is still the same travel involved. Perhaps more.
Another hub and spoke problem is that if you have paid for your hotel, you are certainly not going to another place overnight and having to pay for that hotel on top of your already paid for hotel.
If OP wants to try one place for his two weeks, that’s fine, and he will then have knowledge on how it goes for any future travel plans. Or he could go to one city for a week and try 2-3 day trips and see how that goes. His second week he could arrange as a series of 2-3 day stays.