As you are looking for Bank of America branches address in Round Rock, so on your demand here I am providing same for you:

Bank of America
Palm Valley
1900 E Palm Valley Blvd
Round Rock, TX 78664 US
(512) 716-0106
Financial Center
Monday - Thursday: 9:00 a.m. - 4:00 p.m.
Friday: 9:00 a.m. - 6:00 p.m.
Saturday: 9:00 a.m. - 1:00 p.m.
Sunday: Closed
ATM
Open 24 hours

Bank of America
Gattis School Road
3733 Gattis School Rd
Round Rock, TX 78664 US
(512) 248-5100
Financial Center
Monday - Thursday: 10:00 a.m. - 4:00 p.m.
Friday: 10:00 a.m. - 6:00 p.m.
Saturday: 9:00 a.m. - 1:00 p.m.
Sunday: Closed
ATM
Open 24 hours

For more branches address of Bank of America here is process

Take visit on Bank of America official website

Click on go option which given under location section on the top side

By click there you will land on its branch location finder page which look like given below