In Zug the best things you can buy is food respectively pastry:
The famous Zuger Kirschtorte (a cake filled with kirsch). Places to buy: Confiserie Speck, Konditorei Meier, Konditorei Treichler/Heini.
Speckli (Pastry with almond-taste). Places to buy: Confiserie Speck.
Bsetzi Stei (small Chocolates with a bit of alcohol flavour). Places to buy: Aeschbacher Chocolatier
Chriesiblüete (something like a little Kirschtorte coated with chocolate)
Restaurant Bären, Baarerstrasse 30 (Next to the train station), ☎ +41 41 711 09 43. this is a very old restaurant. The interior is still the same as decades ago and will take you back in time. The food is tasty and you will get big portion for the price.
Restaurant Brandenberg, Allmendstrasse 3 (Directly next to the youth hostel), ☎ +41 41 711 95 96, . This is an institution in Zug. Once a restaurant for farmers, this place is extremely popular in the summer, when you can drink a beer outside below the trees. During the "Stierenmärt it's full of farmers, a real authentic Swiss experience.
Restaurant Freimann, Letzi 27 (Out of town next to a farm, but worth the trip), ☎ +41 41 741 35 10. This restaurant has the rustic charm of a farmer's house out in the green. In the summer it's a pleasure to sit in the beer garden below the trees and drink a beer and eat a "Cordon Bleu". You will get great value for your money. The menu covers the whole range of good Swiss food. The restaurant inside is quite small. On weekends it's recommended to reserve your table, especially if you want to eat inside.
Restaurant Gotthärdli, Seestrasse 3 (Before you enter the old town near the lake). is very small, but with old interior. Very charming. Italian food.
Ristorante Liguria, Fischmarkt 2, ☎ +41 41 710 24 24 (email@example.com), . The restaurant isn't cheap, but with maybe the best view over the Lake of Zug. Has big windows. Fish food.
Chicago Bar, Baarerstrasse 63, . Relatively a lot of space. Comfortable couches and very stylish interior. Very long bar. At some Fridays there are jam sessions which are very cool.(47.17590,8.51713)