My 26yo daughter & I will be traveling for 9 days in August. We plan to leave by train from Budapest to Austria. Not doing Vienna, would like to stop @ Mauthausen for a few hours en route to Salzburg. Salzburg for a few days & some day trips to Bavaria. Kings Castles is a must for her, thinking about Eagle's Nest. Would prefer smaller villages, lakes, mountains to explore. Should we move on to another base site in Bavaria for a few days instead of back & forth to Salzburg? After that, we were thinking of traveling through Switzerland via train w/ a couple stops. Need to fly to Portugal & it seems that Geneva has the most economical flights. 3ish days each for Salzburg, Bavaria, traversing Switzerland. Any advice, thoughts,etc greatly appreciated! Also have been researching rail passes, train & bus tickets for this itinerary & am so confused. So any help in this area would be great, too. Thanks so much in advance! Oh, BTW, she will be in Budapest for a month prior (doing research for PhD) & then needs to be in Portugal for same, hence our start/stop locations.
Use the Man in Seat 61 website for train ticket advice. Rail passes make zero sense economically. Buy point to point tickets or regional tickets, like the Bayern Ticket, for local travel.
IMHO much too ambitious. You are underestimating travel time. Each stop "en route" will cost you roughly half of a day. Book your airline tickets first, so you have a set date for making plans right until then. I doubt that anything in Switzerland is economical, but I have not checked the airfares.
Go to https://www.kayak.com/flights and check flights to Portugal departing from different cities, e.g. Munich, unless you insist on traversing Switzerland.
Forget Eurail passes, an expensive experience for a little bit of comfort, having not to buy individual train tickets. Buy train tickets online in advance, and you will get reasonably priced tickets, sometimes even cheap bargain offers.
I haven't been to Eagle's Nest, but might skip it again, since your time seems short. Salzburg to Fuessen by train takes 4 hours one way, so I'd prefer to move hotels and not double back. It doesn't make your next connection to Switzerland any easier, however. Trains from either Fuessen or Reutte in Tirol to Luzern, for instance, take about 7 hours with multiple connections.
It's hard to make a mathematical comparison without the Swiss destinations filled in. Swiss Travel Passes cover more than just trains, including potentially expensive mountain lifts. Switzerland also offers a lower-investment Half-Fare Card (same link) that you could use within those borders. It's pretty common for visitors to buy one of these options, even if using separate train tickets to reach Switzerland.
Or a Eurail Global pass for 5 travel days within a month probably covers all your train rides and provides some mountain transport discounts in Switzerland. At 26, your daughter qualifies for a youth discount on Eurail passes and might buy a few days more than you, if she would have any separate travel within Hungary or Portugal. Train tickets are cheap in both Hungary and Portugal, but so are extra days on the pass. Global passes have a 5% discount on offer now (nonrefundable product), so that the Youth rate becomes 3 days in a month for $178, 5 for $229, 7 for $272, or 10 for $325 in 2nd class.
Make a concise schedule of your whole trip first, define the travel routes, evaluate the costs, and then you will see whether a Eurail pass will pay off. In my opinion, it won't.