Public transit in Vienna.
Wiener Linien runs a fantastic public transit system. Check the prices for the various multi-day passes. We always by a weekly pass for each person if we will be in town for a whole week (Monday-Sunday) or a monthly pass if we will be in town for a whole month. These passes pay for themselves with just one round-trip on public transit per day. Note, they don’t tell tourists about these passes, just ask for a “Wochenkarte” or a “Montaskarte”.
If you are in town for parts of weeks, then consider the 8-day pass. This pass is much more expensive than the weekly pass, but can be used on non-consecutive days or by more than one person. It needs to be stamped once each day for each person travelling. Note that multiple people using a single 8-day pass have to stay together when travelling.
Austrian carriers all use GSM, the same standard as AT&T and T-Mobile in the USA. If you have a phone from one of these two carriers it may work in Austria, you should check with your carrier.
An iPhone with an AT&T plan will definitely work. However, the roaming charges from AT&T are outrageous. If you are leaving the AT&T SIM in your iPhone, make sure to disable data roaming (look in Preferences). Another option is to use a Austrian SIM while you are in Austria.
Renting an apartment
If you will only be in Vienna for a few days, check out Benedictus Haus for inexpensive rooms in the heart of the old city.