another big vote for Speyer - many of the great reasons are in previous posts above.
As old as the Dom in Speyer is, it amazingly looks like it was just built (it wasn't). And it is practically on your doorstep.
It will be too late in the year for the Goat ceremony, but we really like the little town of Deidesheim, about 45 minutes west on the Wine Route. We don't drink but we love it around there. In Deidesheim, not only is there the Goat ceremony but beautiful half timbered architecture, and a really cute travelling fountain and sculpture on the south side of town. It has a train station and nearby villages are good too, even including Bad Dürkheim which has its own attractions. Bad Dürkheim specialises in big, really big and small. World's largest roulette wheel, world's largest barrel, Germany's largest wine festival which strangely calls itself Wurstfest. Not one salt spring but seven, which makes for opportunities for a salt water spa; and it has the huge Saline which cleans the air. For small, it has a narrow gauge railway.
That whole area is lovely.. I bet in early October the leaves will be beautiful. Car would be faster and easier because the little train goes all around the houses between Heidelberg and Deidesheim and Bad Dürkheim.
In the spring and early summer the fields between Deidesheim and Speyer is just acres and acres of asparagus, and roadside stands to be replaced later in the year by cherry stands, and then cut-and-carry flower fields. A lovely part of the world.
Frankfurt has plenty to see, and the villages around it. The new Altstadt has absolutely gorgeous - each piece of slate is cut to shape. Thousand and thousands of them. Frankfurt on Foot https://www.frankfurtonfoot.com/ give great tours - I speak from experience. There are often concerts in Frankfurt too. Heidelberg to Frankfurt is just about an hour either by car or train. I've been rather unlucky finding easy parking in Frankfurt - the train is very easy.
I hope that you and your friend have a yummy time, and that you get to make your relocation and it is successful too.