suggestions on salzburg and vienna

Assuming you're spending the night in Salzburg, and this isn't just a day trip, I would think the first thing you would want to do is check into your hotel, or at least drop your luggage there. Then go to whichever place closes first. And since you need lunch, to, don't forget to allot time for that.

according to my hotel, it's a 17 min walk from the train station, 11 min walk to the fortress, and under 10 min walk to the old city locations. If it's best to visit Hellbrunn first, i can pay the 5 or so euros and store my luggage in the station.

You could maximize your time by using public transport instead of walking.

you mean from the train station to the city center? would you happen to know what bus does that? thanks!

I don't know which bus it is, but here you can find all information about public transport in Salzburg:
https://salzburg-verkehr.at/timetables/downloads-en/?lang=en

There is a Tourist Information in the Salzburg train station, they can tell you what bus goes where, give you a map, tell you where to buy tickets, etc., we found them very helpful when we were there last year. Lots of bus stops right outside the station.

1. From the train station in Salzburg to to the Hohensalzburg Fortress you can take bus 0-3 direction Salzburg Sud, bus 0-6 direction Parsch, or bus 25 direction Grodiguntersbergbahn and get off at the Rathause stop, then walk 12 minutes to the Funicular that goes up to the fortress. The same bus 25 goes to the Schloss Hellbrunn also so you can take it for both if you want. Go online to www.festungsalzburg.at to buy a ticket for the fortress that will include the funicular ride. You may be able to reserve an entry time for the fortress or late afternoon. This is the website for the Palace:
   
   https://www.hellbrunn.at/en/opening-times-and-information/#prices-opening-times
   Ticket prices at the palace are 12.50 euro for adults. Some online sites charge more for entrance tickets. Maybe you can do a search to find an online sales point for that price plus a service fee if you want to buy in advance.

2. For Vienna, I purchased a Sisi Ticket for me and my wife for September. It covers entry to Schonbrunn Palace, Hofburg Vienna, and Imperial Furniture Collection so would save some money and will allow you to skip the lines at the ticket counter and proceed to the entrance. https://www.imperialtickets.com/en/schoenbrunn-palace/sisi-ticket/53

From my experience the Kunsthistorisches Museum seldom has any long queues. Schonbrunn only does guided tours, so it would be more advisable to arrive early or book a slot in advance if possible.

We were just there in July. Everything is very close to each other, so you have time to take your bags to your hotel. Then I strongly suggest going to the trick fountains first. Maybe even see if you can buy tickets before your trip so that you aren't disappointed, for they were the highlight of our entire trip (we went on to Munich)!!!!! I have toured so many gardens, and have never seen anything so fun! Our family kept laughing the entire time. :) The bus is an easy ride from town too. The fortress is a quick walk once you get back from Schloss Hellbrunn. It reminds me of many other fortresses, so you can zip through it if you start to run out of time. Also make your dinner reservations before you go, as all the best places book up. Our best dinner was at the Funky Monkey. Lunch at Zirkelwirt was good too. Have fun!

3 days is not enough even for basic Vienna but If you are there I would suggest not to visit Hofburg AND Schonbrunn palaces. You can visit just Hofburg palace and Schonbrunn gardens. Schonbrunn palace is sometimes crowded. Also you have to know that Schonbrunn is several kilometres away from center so you will lose at least an hour on road there and back even on super efficient public transport. There are no tickets for Schonbrunn gardens visit but allow at least 2-3 hours even for quick visit (including say Gloriette, Roman ruins, Palmenhaus...) There are no big queues for Kunsthistorisches museum (ticket is 14-15 euros I think, but it is worh it). You need at least 3-4 hours but if you are short with time visit highlight of the collections and leave the rest for some other time. Even the interior of the building without collections is worth the entrance price.

In Sept, we did not encounter any lines at Hofburg Palace or KH Museum. The Cafe at the Museum has the most beautiful setting of any place I've ever eaten and the salad I had was really good. We also really liked the Cafe at the Hofburg.