The IRS put levy on my personal acct and my business acct for back taxes. Can I go open a bank acct at another bank and will they do the same there when I open with my ss#

Yes, they will follow you to the new bank - but it might take some time.

Yes, they will find it. I know you may want to open another one but you may be better off to pay cash for things and try to work on a payment plan with the IRS. And I may be wrong on this but some banks may run a check on you before they let you open a checking account

Yes, they will garnish it as soon as they find it

Even if you are successful in getting a new bank account it won't help. As others said, they will find out about it. And that may make things worse! The IRS can also seize your car, your house, your wages, your retirement accounts, the cash value of life insurance, etc. So if they are coming after you the sensible thing to do would be contact them and work out a payment schedule.