Can someone recomend a b&b or small hotel in the old city center of Basel ?
There aren't many B&B's in the very centre, most B&B's will be further out.
You can look up accommodation on the official website: https://www.basel.com/en There is a box to ticket to select "Bed & Breakfast" only. Make sure you get somewhere that is actually in Basel, this site also lists suburbs and villages further out, some of which have limited transport or longer journeys into the city centre.
One small hotel in a good location near the river I have had positive feedback on the the Resslyritti: http://www.resslirytti.ch/en/
There are many others.