You'll find the museums and attractions on your own, here's a list of the places you don't want to miss for dining and drinking;
Augustiner Brewery is an absolute must. I love this beerhall and have been there in 2000, 2013 & 2015. It's one of my favorite places in the world. As you enter, there's a bit of a food court. A la carte meals are delicious and inexpensive. For your thirst, buy your ticket, grab your bierkrug (no one calls them steins, a stein is a rock in German) rinse your bierkrug, then bring for a fill. The monks brew the beer.
http://www.augustinerbier.at/index.php?id=1&L=1
Bärenwirt- This is totally on my buddy Lee's recommendation. We walked by it on the way to Augustiner but never stopped in. Lee went there a couple days after I went home last year. I emailed him today and he said you "must...must....must" go there. He claims it is in his top ten list of restaurants worldwide. I trust his judgment on this. According to their website, they have been around since 1663 so they've had enough time to get it right. I have to go back soon just to try it for myself.
http://www.baerenwirt-salzburg.at/
https://www.tripadvisor.com/Restaurant_Review-g190441-d694327-Reviews-Barenwirt-Salzburg_Austrian_Alps.html
http://www.yelp.com/biz/b%C3%A4renwirt-salzburg
Stieglkeller - We ate and drank here last year. It's near the funicular that runs up to the fortress. There are some great views from the restaurant. Highly recommend.
http://www.restaurant-stieglkeller.at/en
Zipfer Bierhaus - We went here in 2013- city center
http://www.zipfer-bierhaus.at/en/
You haven't been to Salzburg until you've eaten a Salzburger Nockerl. You'll want to order one and split between yourselves. We got ours at the Hotel Zur Goldene Ente (The Golden Duck) They changed the name to Hotel Goldgasse. I'm sure other places serve it as well.
http://www.dw.com/en/salzburger-nockerln/av-17361879 (to see what it is)
http://www.hotelgoldgasse.at/en.html
Andreas Hofer - This is a cool little wine bar on the Steingasse, It's only a few doors away from an upscale whorehouse that has been in existence since Mozart times. We visited in 2013 (the wine bar, not the cat house).
http://www.yelp.com/biz/hofer-andreas-weinstube-and-restaurant-salzburg?search_key=75173
http://www.dieweinstube.at/
Gasthaus Zur Klause am Tor - We found this hotel bar by accident. It had a funky Bohemian vibe to it. Almost a dive, but not in a scary way at all. We all liked it, for drinks anyway. I'm having trouble finding any info on it in English, which is sometimes a hint that it is more of a place for locals. Not sure if it would be your scene but we had a good time there.
http://www.salzburg.com/wiki/index.php/Gasthaus_Zur_Klause_am_Tor
BOSNA - The most excellent street food in the world. Look for it. You will find it. Cheap and delicious.
https://en.wikipedia.org/wiki/Bosna_(sausage)
Nordsee - If you tire of schnitzel and wurst (I can't fathom that, actually) Nordsee (the Baltic Sea) is basically a fast food seafood restaurant. It's very good, actually. We need this chain in the US. It's surprisingly yummy. We also snuck in to use their restrooms a lot.
https://www.tripadvisor.com/Restaurant_Review-g190441-d6594580-Reviews-Nordsee-Salzburg_Austrian_Alps.html
http://www.nordsee.com/at/
That should get you started. Now find some of your own favorites too!