BTilke

I think a trip to Vienna/Prague in March sounds terrific!! For the last four years in a row, I've been going to Vienna in March and always found a LOT going on. The weather ranges from sort of mild to cold and snowy, but Vienna in the snow is beautiful. It's a good city for a woman to visit alone, too--I've always felt very safe walking around alone at night (in the main areas, of course). However, keep in mind for trip planning purposes that there is a fairly large conference in town March 5 to 9, which will take up a good chunk of the hotel rooms. So plan on arriving after March 10. You have many side trip options from Vienna, i.e., Prague, which you already noted, plus Salzburg, Graz, Budapest, etc.
You will find some hotel deals for March travel in Vienna, too. For example, the Marriott has prepaid rooms available for 125 euro per night; the Kaiserin Elisabeth (a traditional hotel with about as central a location as you could hope for) has singles available in March for under 100 euros per night, breakfast and tax included.

mamc

I agree with those who suggest Rome. The weather is likely to be better than further north. And you will enjoy Rome so much that you will convince your daughter and friends to return with you soon.