Another couple of options from the French side....
Au Petit Paradis - Hausgauen (approx 25 min drive from Basel).
Owned by a fiercely proud French Caledophile (she plays the bagpipes and EVERYTHING), this is a charming French restaurant set in the idyllic Alsace countryside perfect for cosy dinners as well as large events (weddings, work dos etc.). They have a 'Menu Secret' which is pretty decent value. Very helpful for assistance with the wine selection, without being sniffy (which can be tricky to find in some parts of France )
Check out the photos here: http://aupetitparadis.fr/
Restaurant Au Lion d'Or - Rosenau (15 mins drive from Basel)
Just a great selection of tasting menus, topping out at EUR49 for a full-on FEAST (snail-lovers, you're in for a treat). Great wine list. Great French classics - bring on the foie gras. Steak that is cooked tremendously. If you need a palette cleanser, consider the Trou Alsacien, which should poke a 'hole' in your stomach to fit in the outrageously delicious pudding selection plate. And if you're into digestifs... you should see the selection....
www.auliondor-rosenau.com
One more for Germany -
A bit further away this one, but the drive itself is so spectacular it's worth it... I promise...
Restaurant Adler - Baerental (by Feldberg) in the Black Forest
It never ceases to amaze me just how nearby the Black Forest is to Basel. It's easy enough to cruise up the motorway to Freiburg, but taking the 317 from Loerrach, to Todtnau, to Feldberg takes you right into the heart of this fantastic scenery, which looks stunning any time of the year (when the leaves start to turn it is pretty fantastic... but I digress).
This place can get booked up in the summer, or when the Baslers/Zurchers drop in for a taste of autumn (kuerbis and boar, what a great combo) so it's worth making a reservation. If you're lucky, you'll get a table by the window overlooking the valley, resplendent in the late summer sun. Most of the ingredients are sourced in the Black Forest so it's mildly satisfying to think that your plate hasn't come through the cold channel via Singapore to get to your fork.
Location is fantastic, with a great local wine list and a legitimate cup of espresso to wash it all down with. If you're really getting stuck in, they have several rooms upstairs if the drive back to Basel (50 mins) seems a bit much.
http://adler-feldberg.de/en/restaurant/