There is a the München Welcome Card Partner 3-Day-Card Total Area for EUR 48,00
This ticket covers local public transport in the complete MVV area for 3 days and gives discounts for many sights/attractions (see linked page).
If you buy it on We 1. March it will be valid till Sa 4. March 06:00 (6am).
There is no 3-day ticket which covers "only" local public transport for the complete MVV area, only one day tickets.
Normal single ticket to the airport is EUR 8,80. A Partner-Tageskarte (mini group day ticket) for the whole MVV area is EUR 16,00. Thus cheaper than 2 single tickets.
The route the ICE 3 trains use is Munich - Augsburg - Ulm - Stuttgart.
Thus Augsburg is the first and closest stop.
All 3 cities are worth a visit.
Not all ICE connections towards Stuttgart are by ICE-3 trainsets. You have to check the comlete itinerary of the train. If you check out the details of a connection with the DB timetable you can click on the train number, than a new window with the complete route appears. A part of the route must be "Frankfurt(M) Flughafen Fernbf - Siegburg/Bonn - Köln Hbf". This is the highspeed line between Frankfurt and Cologne which can only be used by ICE-3 trainsets.
Munich to Augsburg and Ulm has been always a fast train line (up to 200 kph), but is not a dedicated high speed line. Ulm to Stuttgart goes through the Swabian Alb, scenic but not fast.
End of May 2006 the new high speed line Munich to Nuremberg will be taken into service.
If you buy a return ticket in advance you can get discounts. A "Sparpreis 25" ticket Munich - Stuttgart and back for 2 adults is EUR 103,50 (normal return ticket is EUR 184,00).
DB has also sometimes special offers valid just a month or so.
Than there are the Surf&Rail offers. You can book on Saturday return ticket for alternating routes for the next week. This week Munich - Stuttgart and back was on offer for EUR 39,00. But this route is not in the pool for next week.
http://www.surfandrail.de (despite this name only in German)
(Surf&Rail timetable + booking; at least here you can switch to English)
Or consider a budget flight trip to Cologne sometime in the future. Cologne is a big hub for budget airlines. It's different (not only that the beer comes in 0,2 l glasses compared to 1 l mugs in Munich). And it's obviously on the highspeed line Cologne - Frankfurt.
Interesting is the "loop" one leg the highspeed line and the other leg the Rhine valley route.