We're somewhat local to Prague and have been there many times. One of my favorites that I did last time around was to go up to Petrin (using the Petrin funicular) and then walk to Strahov (this is the site of an old monastery). There's an interesting museum of miniatures you can go to (muzeumminiatur.cz), or just grab a beer and enjoy the view. You can then walk towards Prague Castle, coming from the less common direction. We then usually walk through the castle and down towards Malastranska. If you can, I would recommend going to the crypts and up the tower in St. Vitus Cathedral. Hopefully they are open. If you google map the route, it's pretty easy to see.
Crossing Charles Bridge and going up to the castle is also nice and a more common route. You start at Wenceslas square, go to Old Town Square, cross the Charles Bridge and then up to the Castle.
A great place to grab food in Malo Stranska is the Malostranska Pivnice (
Malostranská Pivnice). I haven't been there in many years, but at the time it wasn't much of a tourist trap and the prices were reasonable. They also have another place in Prague called U Vejvodu. One general tip I use to determine if a restaurant is expensive or reasonable is to see how much they charge for beer. I expect beer to cost about 35-40Kc for 0.5 liters. If you see places charging 90Kc+, then you know you're at a place that is catering towards tourists. I haven't been in Prague for a few years, so this may have changed some, but not by much.
As for local Czech dishes, a favorite of ours is Svickova. From the Malostranska Pivnice menu they translate it as "Mrs Müller’s home made roasted sirloin of beef with traditional Czech cream sauce, bread dumplings." But the Goulash, Fried Pork (Wiener Schnitzel for the Germans in the audience) and Knedlo, Vepro, Zeli (Dumplings, Pork, Cabbage) is also another good alternative. Even though I don't see the latter on their menu, other places will have it. And if you're looking for something without meat, a Czech favorite is Smazeny Syr (Fried Cheese), usually served with fries. Another good vegetarian dish is Smazeny Kvetak (Fried Cauliflower), but that might be less common.
Mid-May should be a great time to visit. If you have any questions, free free to PM me. Enjoy your trip!