Find your hotel and relax after a day of travel. I can find a nearby restaurant and playground.
Hotel: AirBNB

Zoo
Get the kids out somewhere they will love early, like the Basel Zoo.
Old Town
Walk around central Basel today and visit Basel Old Town, the Natural History Museum, and Kannenfeldpark.
Take the 1.5-hour train ride to Überlingen and check into your AirBNB and rent bikes for a longer stay here. There is a cycle path around Lake Constance, so you can rent bikes in town at one of these places:
https://www.cycling-lake-constance.com/bike-rental-workshops#ueberlingen
Hotels: Überlingen AirBNB
Rail: RailEurope (Routes with 2 stops at 8:43, 10:43, and 12:43. Short layovers of 10-20min)
Spend the day enjoying lake life. Old town is about a 15min walk or 5min bike ride from a couple of lake beaches: https://www.ueberlingen-bodensee.de/strandbaeder
There are some nice lakeside playgrounds too:
https://www.ueberlingen-bodensee.de/uferpark
And this thermal bath in Uberlingen seems to allow children of all ages – though Google Translate had difficulty with it:
https://www.bodensee-therme.de/familien
If you need a day trip, visit the Sea Life Konstanz Aquarium, which is 1 hour by train each way in Konstanz.
Spend you last day on the lake and exploring gardens.
Train: RailEurope (Departure at 9:10am. Short 10min layover.)
Hotels:
Beirgartens
Freiburg is a university town, so there is plenty of beer. It’s also a popular wine region.
Seepark
Central park with small lake, playground, and restaurants.
Münstermarkt
An outdoor farmers market is open every weekday morning.
Titisee (Baby Lake)
A charming lakeside village near the city with a Ferris wheel. There is also a water park in the main town if you want more activity. Gaststätte Bootshaus is a nice lakeside cafe and beirgarten.

Southern Black Forest National Park
The Southern National Park is actually the largest park in the Black Forest. These are somewhat hard to access without a car and with children, but there are a few popular trails you can access from a train station like Ravenna Gorge. You can also explore the nearby town of Hinterzarten.
I think you might just want to hang around town on your last day and live like a local. However, if you still want to get out there are other options.
Steinwassen Park
If you’re not sick of zoo theme parks, there is another option nearby at Steinwassen Park.
Take the 3-hour train ride to Frankfurt and check into your hotel. You don’t want anything at the main train station, so I would consider taking the afternoon train to Frankfurt and staying directly at the airport. That will allow you to get some extra sleep since you can walk right to the terminal.
Rail: RailEurope (There is a direct at 13:56 that might be a good option.)
Hotels:
Wake up and transfer to the airport for your 10 am flight.
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