Bangalore to Kanchipuram road distance is about 280km (via Hosur) and about 260km via Chittoor.
Route 1: Bangalore --> Hosur --> Krishnagiri --> Vellore -->Arcot --> Kanchipuram : 280km
Route 2: Bangalore -->Hoskote --> Kolar --> Chittoor --> Walajah --> Kanchipuram : 260km
Route 1 is faster with almost 4 lane most of the way.
For train, the nearest railway station on the Bangalore to Chennai route is Katpadi Jn and Arakkonam Jn. Most of the express trains towards Chennai stops at Katpadi, and some at Arakkonam. By the way Kanchipuram has a rail link, a few passenger trains and a couple express trains to Madurai connects Kanchipuram by rail.
Here is the list of best 16 temples in Karnataka