Are there cute little towns we would like to stop at along the way?
I take it you are staying at least overnight in Innsbruck.
The most adorable town I can suggest is just across the border in Germany, a direct train ride from Innsbruck of less than 1 hour: Mittenwald.
https://www.alpenwelt-karwendel.de/en/mittenwald-bavaria
A mountain lift (Karwendelbahn,) river gorges, a violin museum (Mitenwald's commercial claim to fame is violin-making.)
Have you considered Rick Steves' suggestion for staying in Reutte? Reutte is about 1.3 hours by train from Mittenwald on your way to Füssen; Bus #100 gets you from there to Füssen in less than 30 minutes. Reutte is a reasonable place to stay if you also want to visit Ehrenberg Ruins, Highline 179, and to take cable car rides into the mountains. See his book and this page:
https://www.tripadvisor.com/Attractions-g580114-Activities-oa0-Reutte_Tirol_Austrian_Alps.html
If this were my trip, I'd spend a full day/night in Mittenwald, then take the train to Reutte for however many nights you might want there.
Both the Innsbruck > Mittenwald and Mittenwald > Reutte train rides are scenic routes and quite cheap using small-group day passes that you can buy right at the train station.
Below is a rail map showing the Innsbruck > Mittenwald > Reutte i. Tirol train route I've described:
https://www.dbregio-shop.de/uploads/files/RTWerdenfels_Streckenkarte.pdf
The final route to Reutte is a ride that some take just for the sightseeing it provides:
http://www.erlebnisbahn.at/ausserfernbahn/infos/DB12029.jpg