Step 1:
Vaishali and Rajagriha (Rajgir) are historically important places in Bihar.
Step 2:
Sarnath is in Uttar Pradesh, Sanchi is in Madhya Pradesh, and Ellora is in Maharashtra.
Step 3:
Only Vaishali and Rajagriha belong to Bihar.
Step 4:
Therefore, the correct answer is:
\[
\boxed{\text{(2) A and E Only}}
\]