I would be moving to Basel on a long term assignment soon. I am interested to know about the Income Tax rates ? Is there any allowances for staying with Family and Kid ?

have a root around in here, suggest you use the search term Basel on the forum search.

http://www.englishforum.ch/finance-banking-taxation/

You might want to look for an apartment outside of Basel in the Canton of Baselland. Taxes are A LOT lower there (20-30%, especially if you're married and your wife works as well) and there are plenty of communities with direct tram lines to Basel (Binningen, Bottmingen, Oberwil, Therwil, Allschwil etc.)

peter