There is some Hotel around the Jewish area. If you looking for Hotel with no electric door etc. (for Shabbat) then Hotel Steinenschantze is for you:
Hotel Spalentor
Schönbeinstrasse 1
CH - 4056 Basel
Tel: +41 61 262 26 26
if you look for Hotel near the university hospital please try this:
Bed & Breakfast
KiwiHomes
Eulenstrasse 81/83
Ch-4051 Basel
Mobil: + 41 79 790 88 88
Fax: + 41 61 281 00 00
http://www.kiwihomes.ch
for more options click here