Need help creating itinerary for 3 weeks in Switzerland

Also, this will be the first time I will be in Europe for more than three months within six, so does that mean I need a visa? Where might I buy one? AAA perhaps?

You don't just "buy" an extended stay visa, you apply for one at a European country, explaining your reasons, show proof of income, medical insurance etc. Where are you intending to go for that length of time?

Traveling with only your passport, you are allowed to stay in the Schengen Zone for 90 days in a rolling 180 day period. You can't buy a visa. If you need to stay in the Zone for more than 90 days you have to apply to a specific country within the Zone for a long-stay visa. Depending on the country there are a variety of visas. It is a long, arduous process, and different countries have difference requirements and restrictions. Unless you REALLY need to stay there this is probably more trouble than it's worth. Here's an example of the requirements for France in applying for a long-stay visa. You can see how laborious the process is.
Most people who are going as tourists just use countries outside of the Schengen Zone to help stretch out their 90 days. The UK is a great place for this...you can stay there for up to 6 months using just your passport. If this is part of your itinerary it may help you stay within the 90 day limit. Here's a map that shows which countries are in the Schengen Zone and which ones are not...it may help you plan your itinerary. You don't want to overstay the 90 days...you will be fined and banned from Europe if caught.

Brenda, first to reinforce what the others said. A Visa is not something you buy like a rail pass. It is official permission to enter a country and stay there for a specified period. When you get a visa you are applying to live there as a temporary immigrant. Hence a lot of legal requirements, paperwork, time and cost. You apply to the government of the country you wish to stay in, and their immigration laws apply.
Some countries agree to not require visas of each other's citizens. For example citizens of many countries (which I assume includes yours, you don't state your nationality) can enter the Schengen Area for 90 days in any 180 without a visa; and in return EU citizens can enter those countries without a visa. Citizens of other countries require a visa from day one.

To get back to your original question. Are you staying the complete 3 weeks in St. Gallen? A curious choice, unless you have friends/family there. Normally I would ask where you are coming from (entering Switzerland from), where you are leaving to and try and fit a circuit of Switzerland around that. But, if you are stuck in St Gallen all the time, you are limited to where you can go as day trips.
If it is friends/family you could ask your hosts for suggestions. In that corner of Switzerland I would suggest:

• Bernina Pass Railway. To Chur, then Over the top of the Alps to Tirano. Back same way. Long day.
• Bodensee (large lake north of St Gallen). Towns: Lindau, Konstanz, Bregenz. Boats on lake. Insel Mainau.
• Stein am Rhein
• Appenzell area. Some nice mountains with cable cars up.
• Luzern (long day trip). Boat and /or trip up mountain.

I have not listed the Berner Oberland, Glacier Express or anything in Romandie (Western Switzerland) or Ticino (south face of the Alps). All too far for a day trip from St. Gallen.

Look up train times on the SBB website: https://www.sbb.ch/en/home.html

Vienna: A long but scenic train ride from Switzerland longitudinally through the Alps. But worth it. You need a number of days in Vienna. The route goes through Innsbruck and Salzburg, both of these are worth a day or two en route.

From a "must see" standpoint, I can't recommend the Berner Oberland area enough -- it was our favorite place in Switzerland and you can easily access it through public transportation with trains/gondolas (and all around the area). If you want to see the Swiss Alps, this is the place to go and we stayed in Murren, about 6k up on one side of the mountains. I think Lucerne is worth a day or two and you can also access that by train, but it is EXPENSIVE. And we also thought the Lake Geneva area was pretty both around the lake and then into the countryside (e.g. Gruyeres) -- rolling green hills dotted with sheep and Swiss chalets. And if you're into castles, the Chateau de Chillion is on Lake Geneva near Montreux that is worth a stop if you're in the area.