In Alsace -- Colmar, Kaysersberg/Riquewhir/Ribeauville/Eguisheim (bus from Colmar), Selestat, Château du Haut-Kœnigsbourg (private shuttle from Selestat train station), Neuf Brisach (UNESCO site, well-preserved impressive fortified town/citadel designed by Vauban. Tourist office offers guided town/ramparts walk. https://www.visit.alsace/en/246001403-neuf-brisach-fortified-town/.) Alsace has cheap 24 hr tickets for unlimited TER and city buses -- https://www.ter.sncf.com/grand-est/offres/forfaits/alsace/alsace_alsa-plus
Farther in France -- Nancy & Metz (I visited both in one long day-trip)
In Germany -- Esslingen/Ludwigsburg (both are right outside Stuttgart, Stuttgart is 1 hr ICE/TGV train ride from Strasbourg), Gengenbach, Baden-Baden, train ride thru prettiest part of Black Forest (Hausach -- Donaueschingen) all the way to Konstanz, Lake Constance towns (Knostanz, island of Minau, Uberlingen, Meersburg, Lindau). You can visit all these towns using Baden-Württemberg-Ticket for up to 5 people, unlimited local train ride in one day. https://www.bahn.com/en/view/offers/regional/regional-day-tickets.shtml.
https://fahrkarten.bahn.de/privatkunde/pauschalpreisbuchen/pauschalpreis_start.post?lang=en&country=GBR&redirected=1&dbkanal_007=L04_S02_D002_KIN0060_REGIO-LAENDERTICKETS-KARTE-BAWUE_LZ03#stay.
Baden-Württemberg-Ticket train network map -- https://www.bahn.com/en/view/mdb/bahnintern/angebotsberatung/regio/laender-tickets/pdfs/2018/mdb_270079_streckenkarte-badenwuerttemberg_a2-bwegt-look-rz.pdf
Baden-Württemberg-Ticket does not cover Strasbourg. You need to take Strasbourg tram D to Kehl Bahnhof which is 15 min ride from Strasbourg historic center to get on the SWE train at Kehl. I would recommend 1-2 nights at Konstanz.
There's a all day ticket that covers both Alsace and Black Forest area -- The RegioElsassTicket is valid on DB Euregiobus 1076 b/w Colmar-Freiburg and in the entire area of the Regio-Verkehrsverbund Freiburg (RVF) on all bus and train lines. Also on the Kunegel buses from Colmar to Alsace's Münstertal, to Kaysersberg, le Bonhomme, St. Hippolyte, Rouffach and Guebwiller. This ticket is valid for 24 hours and costs 16 euros for 1 person and 32 euros for 5 people.
Freiburg-Colmar RegioElsassTicket: https://www.rvf.de/fr/fahrkarten-tarife/ueber-die-verbundgrenze/fahren-nach-frankreich/regioelsassticket-colmar-en-bus
Map of all the towns covered by RVF ticket -- https://www.rvf.de/en/fahrkarten-tarife/travelling-with-rvf. This RVF ticket covers 2 towns many folks on this forum often recommend to others: Titisee and Staufen.