If you are getting Anna University no need to look anywhere else. Anna Unuversity is one of the best university in the country and for all courses it is NAAC accredited. 

You apply for B.Arch counselling by Anna University. If you do not get than you apply for B.Arch counselling in chennai 

Hello Dear!!!

If you want to do B.arch i chennai there is no need to go for ANNA University only.

There were many private institutes that were providing b.arch courses.

Examples are vellore institute of technology,SRM,Sathyabama institute of technology etc. You can directly appraoch institutes if you did not write the respective entrance tests.

Thank you