It's a stunning and enchanting city -- surely the culture capital of Ukraine. It was a complete surprise for us.
If you don't know how to read cyrillic, spend an hour or two on the train and teach yourself how to transliterate (memorizing the letters so you can sound out a cyrillic word in English, even if you have no idea what it means). You can do it from the Russian Alphabet page in the back of your Lonely Planet. Nothing in Ukraine is written in the Roman alphabet, and for some stupid reason, most maps (including LP and Let's Go) as well as the hostel directions on this site don't include any cyrillic. Have a great time in this amazing country and thank me later.
Lviv is the first large city on the Ukraine-Poland border coming from Krakow. It is a very nice place to stop for a few days. Its city centre is very small, not unlike Krakow, so everything you want to do and see is easy to walk to. When you are booking your hostel in Lviv, we estimate there are a couple days worth of sights to keep you busy, and if you add in the nightlife, you could stay for perhaps three or four.
Lviv hostels are booming, with a surprising number to choose from for such a small city. There are a number of hostels around the main square and some just off the main street from the Opera House, but really most hostels are so central that you dont need to be on the square to see any of the sights. Watch out for the hostels with very cheap prices (6 euro and lower), there is a reason they have dumped the price, normally they are not up to other hostel standards and attract backpackers with the price, stay at your own risk.
The sights not to miss are the Opera House, which some days can be entered on a tour, or if you are lucky and want to add some culture to your life, can buy a 4 euro ticket to see a Opera there! The High Castle is about thirty minute walk uphill (there is a reason it is called High Castle) and it has the best view of the city. They best time of day to go is in the morning before the clouds and sun block the view. The largest graveyard in Europe is also here. Nearby the graveyard is a village, recreated from eight different areas and times of Ukraine's past. Over 100 houses have been moved to this 43 acre park but yet again no English guides. Some of the hostels do tours to both places (with English guides of course) ask about that when you arrive.
Overall it's a nice city to stop over and visit on your way to other areas of Ukraine or Poland. Lviv should not be overlooked as a stop on your travels.
Getting to Lviv from Krakow is easy, with daily night buses going between the cities. The train also runs twice a day each way and takes the same about of time because of the changing of the tracks (but is twice the cost). The cheapest way is to take a local transport to the boarder and walk across then take train or bus on other side (taking a train on the Poland side or a bus on the Ukraine side).