Lviv was my only destination in Ukraine, I arrived here on plane and left the same route.
The airport is not far from the city center, and there is a trolley bus connecting it with the center. It comes every 10-15 minutes, so it's very convenient. And cheap.
The vehicles of the public transport are not modern nor comfortable, but the timetable infrstructure is surprisingly advanced. You can track each and every vehicle and their routes on a map. This makes it easy to know how to get to different parts of the city.
Regarding the tickets, it works in a peculiar way. You can buy tickets at newspaper stands then you need to validate them when you get on the bus (stamp them). You can also buy one from the driver, but as usual, they prefer if you don't use large denominations.
Before I arrived in Lviv I read about the practice of asking fellow passengers to pass the money to the driver and waiting for the change to came back to you. I could witness it first-hand, and it's especially useful when the vehicle is crowded. People don't need to make their way to the front then to come back. And while money is passed among several people, it's not lost in the process.
But it seems like there are some inconsistencies between individual vehicles. The trolley bus I took at the airport had a terminal where I could use my bank card to pay. But doing so, all I got was a smiley and no printed ticket. When I had to change the vehicle as it broke down, I saw people paying the driver, but they did not get tickets either. I thought this way the way it works, but when I went back to the airport a week later on the same line, tickets were issued.
The restaurants and cafes in Lviv are surprisingly brave in providing an immersive experience which is a nice touch. In certain places, a cafe is not just about tables and drinking coffee but you also get to see the machinery that roasts the beans when you step in. Or you could go down the mines where everybody wears helmets and you can try the fire coffee made using as gas torch.
Or go to the most expensive restaurant where you can get a 90% discount by having the Lokal card. Or a bar where you need to know the password to get in. And you also need to find it as it is "hidden".
Lviv is full of places like these. And while they are the most touristy ones in the city, they are not that expensive.
Accompanying these thematic places, there a card that offers some discounts and a points-collection scheme. You can get it at any participating restaurants/cafes, you just need to ask for it when you ask for the bill. Then you need to fill in a form of registration with some contact data and you'll get the card. I think it was in Ukrainian but I don't remember having problems with it, so it might be in English as well.
There is also a mobile app where you can keep track of your points, but that didn't work. I had some problems logging in, and everything requires Google Translate, so it's not easy to navigate the app and the website.
Ever since I was in Wroclaw I started looking out for dwarves in other places. I've heard there is one in Lviv, but I didn't know where.
It turns out it's not hidden at all, after some walking in the center I found it.