Hi there,
A number of Swiss bank do allow residents of Austria to open private accounts (also known as checking accounts or giro accounts). However, many Swiss banks charge non-resident fees in addition to standard bank fees to customer who reside outside of Switzerland.
Some banks have lower non-resident fees for residents of Austria. The Hypo Landesbank Vorarlberg (Switzerland) offers exceptionally favorable conditions for Austrian customers.
You can request a PDF table which compares the non-resident fees of Swiss banks and lists exceptions and discounts for residents of specific countries at the foot of the moneyland.ch guide to non-resident fees at Swiss banks.
The moneyland.ch private account comparison makes it easy to find the standard costs of Swiss private accounts. Add these to the non-resident fees to find the full cost of holding a private account at a given bank.
Depending on your purpose for opening a Swiss account, it may not make financial sense to do so. For example, if you occassionally need to receive money from Switzerland or transfer money to Switzerland, then using SEPA transfers directly to and from your Austrian bank account may work out cheaper than holding a Swiss bank account. If you make numerous transactions within Switzerland in Swiss francs, on the other hand, holding a Swiss bank account could work out cheaper (taking the EUR to CHF exchange spread and possible transfer fees into account).
Best regards from Moneyguru