Both Würzburg and Nuremberg are on the same route to Frankfurt. You wouldn't have to choose. You could stay 2 nights in Nuremberg and the 3rd in Würzburg. From W'burg you would be only 90 minutes from FRA airport by direct train.
Nuremberg is a particularly atmospheric place with all sorts of interesting sights, museums, etc. Population is around half a million or so. If you only want to stay/see one place, I'd probably suggest staying there.
Würzburg is much smaller than Nuremberg; wine plays a big role in the lifestyle here. There are some small Main River towns nearby you could visit by train - look into Veitshöchheim, Ochsenfurt, Marktbreit. Iphofen is a possibility too.
It would be possible to stay only in Nuremberg and to visit Würzburg for several hours on your way to FRA if you plan to overnight at FRA. Use the station lockers for your bags.
If instead of a large city you want a really low-key stay in a gorgeous little wine town with old town walls and towers, you probably couldn't do better than Iphofen. Stay there and day trip into Würzburg or Nuremberg. Scroll through photos at this German page:
https://www.stadtbild-deutschland.org/forum/index.php?thread/2985-iphofen-galerie/&s=ab4e02c80a93892b673a79750d07ca1a5090d232
There's a public pool facility in Iphofen that your toddler might enjoy: http://tramino.s3.amazonaws.com/s/iphofen/693219/1200.jpg
Baden-Baden: focus is on health spas and casinos, a place popular with the uber-wealthy and the geriatric, sort of a peculiar choice for most people. The train station is well outside town so you'd need to take a bus or taxi as well to get into the center.
