I can recommend 'home from home.' Near Novartis campus on Voltaplatz.
My 2 year old has gone for 1 day a week for a year and a half.
There is a huge personal touch and individuality with this 'krippe.'
She will speak German or English to your child if you wish. It is flexible, affordable and incredibly family orientated, with family days throughout the year.
I may sound like i am on commission, but I am not.
I went to see many krippe's in the basel area. I liked this one the best. You may not. Go and visit as many as you can and talk to the staff/parents etc.
You may probably go back to see Home from Home!!!
Good luck in your search