I love Lviv! My husband and I were there in August and hope to go back this September.
The Lviv skansen (Museum of Folk Architecture and Life) is also known as Shevchenkivskiy Hai. Since you will be there right after Orthodox Easter (April 28) you may have the opportunity to see some of the traditional post-Easter festivities at the Museum. Also, May 4 is Lviv City Day, so always lots going on for that as well.
There is a TI in the Town Hall (Ratusha) on the Market square (Ploscha Rynok) the staff there spoke English, you can get maps and find out about events and tours. Outside the Ratusha there is a little yellow tourist train, the route takes about an hour and I think it was 80 hryvni, about $4. It gives you an idea of what's where and is a bit of a change if you get tired of walking around.
The not-to-be missed cemetery is the Lychakivsky Cemetery, don't miss the graves of Solomiya Krushelnytska (opera singer), Ivan Franko (poet) and Volodymyr Ivasiuk (composer). And new graves of soldiers and volunteers who have died fighting the war in the east - some of them were heartbreakingly young.
The Ploscha Rynok is full of restaurants and coffee houses. We especially liked Baczewski, vul. Shevska, 8 (needs a reservation), Atlas (pl. Rynok, 45), Amadeus (pl. Katedralna, 7)
Also Veronika, Prospekt Shevchenka, 21 and Puzata Khata (there are 2 locations, vul. Sichovykh Striltsiv, pr. Shevchenka, 10) it's a cafeteria style restaurant with good inexpensive food (though May will probably be too early for the varenyky with cherries, topped with sour cream and sugar.....)
Make sure to stop for some cherry liqueur at Piana Vyshnia (pl. Rynok, 11) - that's all they serve, just look for the people standing around the outdoor tables. And buy some gingerbread cookies at Lvivska Maisternia Prianykiv, vul. Krakivska, 14 - or go just to look - they are little works of art, I really liked the ones that looked like embroidery.
Lots of shops around selling vyshyvanky (embroidered shirts and dresses) and other kitschy stuff, but an especially nice store is Mamyna Svitlytsia, vul. Virmenska, 12. If you don't make it to the Carpathian Mountains, it sells a lot of the famous Kosiv ceramics. And next door is a little shop called Lelitka, which sells embroidery supplies.
At 24, Prospekt Svobody in the Opera Passage, 4th floor, is Roksoliana Shymchuk's Etno-Halereya, a shop which is quite pricey but also her private museum. She comes from a family of artists and they have been collecting artifacts for a long time. The collection of embroidered items from all regions of Ukraine is astounding -3 rooms, floor to ceiling, wall to wall - and amazing quality - better than what I saw in some museums. There is a small admission fee, and for an additional fee you get a guided tour, which is very interesting - they are very knowledgable, but I don't know if they have an English language tour.
The open air craft market known as the vernissage near the Opera is also fun to wander through. Also lots of bookstores everywhere, Knyharnia Ye is a chain with quite a few stores in Lviv, they have some English language guide books, postcards etc. Interesting to see lots of English language best sellers translated into Ukrainian.
We stayed at the Ibis Styles on vul. Shukhevycha, about 10 minutes from the Market Square and would happily stay there again. If you are looking for a guide/driver, my husband had the hotel arrange a driver to take him to his father's village about 60 km. from Lviv, I think all the hotels can make these arrangements.
I could go on, but I see I'm almost at the maximum length (we also visited Przemysl).