No hidden gems. My must-sees may not be your must-sees.
I've not attended a Carnival. Basel has one and Basel is a very good visit. Mulhouse has a down in the mouth kind of feel compared to the other places we visited in the area.
With a car I'd rent an apartment in one of the other villages around Colmar. Riquewihr, Ribeauville, Kayersberg and Bergheim are all good choices (Bergheim is quieter, with few shops and a handful of restaurants; I like it).
If visiting Strasbourg, park the car at Selestat and take the train in. Browse for parking in Basel, it's not cheap. We parked somewhere opposite the cathedral, across the river. Another time we parked in Weil and took a short train ride in.
Wissembourg is worth it, though a bit of hike from where you'll be staying. Mt St Odille, yes. Haut Koenigsbourg a definite yes.
Also consider Obernai, Barr, Dambach, Andlau for short visits. March is probably not good for hiking through the vineyards or woods, though many of the paved and gravel roads in and out of the villages were quiet even during September.
Black Forest. Gengenbach and Staufen, for sure, Endingen. Freiburg can use a day (Carnival also?). Schiltach probably out of reach. Decent therme in Bad Krozingen.