Follow my list on Google Maps - Lviv Guide / Rustam

Lviv Coffee Mine - Great place to start the day. It's called a "Coffee Mine" because of it's underground(huge cellar) where you should go first, they provide you with a mining helmet and give a tour around. After that sit and enjoy their amazing coffee in a greenhouse.

Valentino restaurant - Visit during the day. High-end place with amazing food, check out the roof top terrace with a beautiful view of the city.

Gas Lamp - You can start your evening with this place, try a variety of local shots in test tubes.

Kryivka - Go here in the evening. A "secret", hidden place you should ask direction for. Once you found the door without any signs, knock it. There is a pass to enter, which is the Ukrainian salute: "Слава Україні - Героям слава". 
You need to say it when asked in order to enter. They will give you a shot on the entrance. The restaurant itself is a bunker from where various partisan activities were carried out during the fight for the independence. Traditional dishes are amazing and in the evenings there is live ukrainian singing performance.

Masoch - Sado-masochistic themed restaurant with a special guest treatment in a form of ass whipping and adult shows anyone can take part in.

Lviv Handmade Chocolate, search the closest on the map - The most famous homemade chocolate in Ukraine, buy it for yourself and as a present.

Puzata Hata, search the closest on the map - Ukrainian dishes served in a fast-food manner, iconic cheap place you can find anywhere in Ukraine.

Also visit flea markets and churches.