Sometimes it can be refreshing to take a trip across the border just to see what's on the other side. The town of Przemysl is just 5 km or so from the Ukrainian border crossing at Medyka/Schehyni, which in turn is an hour and a half from Lviv. For expats making the proverbial "border run," this border crossing may be a frequent destination anyways.
My preferred way of getting to Przemysl sounds complicated but is cheap and easy. Transportation to Przemysl and back from Kiev costs as little as $30 USD.
Take an overnight train to Lviv from wherever you are. Avoid "express" trains because sitting up for 6 hours is intolerable no matter what movies they show. Platzkart (3rd class) will be roughly 100 UAH ($13 USD) from Kiev, and kupe (2nd class) will be roughly 160 UAH ($20). Kupe typically has air conditioning, which can make a huge difference in summer.
Just outside the Lviv train station to the left of the main entrance is the bus to the border. If you don't dally getting out of the train, you'll probably get a seat. It's 15 UAH to the border ($2 USD) and just under an hour 40 minutes.
From the bus station at Schehyni (the final stop), retrace the last 100 meters the bus drove, turn right, and pass all the currency booths and insurance companies to reach the pedestrian border crossing. Procedures seem to have been streamlined in recent years, and it usually takes just half an hour to get to the Polish side.
There you'll find an ad hoc market area that looks pretty much like the Ukrainian side, with numerous locals holding up one bottle of vodka and two packs of cigarettes apiece. This is the maximum amount allowed, and they cross the border each day to sell inexpensive Ukrainian spirits and tabacco at a profit to Poles who drive by in cars looking for a good deal.
Next time I'll have to try it, too, for fun. You may end up waiting a few hours for a customer to show up, though, which can be a pain. You might also get a few elbow jabs as you crowd up to people's car windows trying to be the first to sell your goods.
With 2 zloty in hand ($0.60 USD) enter the bus that comes by every half hour or so taking people from the border to the nearby town of Przemysl. To get back, repeat all these steps in reverse.
Przemysl is an ancient Polish town of great historical importance, almost up there with Krakow and Lviv (wait, we all thought that was a Ukrainian city, right?) due to its strategic location at a natural geographic crossroads between Central and Eastern Europe. It's got a charming historical center with a bunch of old churches and museums, as well as the "only sloping market square in Europe." Well, every town's got to have its claim to fame.
Przemysl's got a few things going for it over Ukrainian towns, as well as a strike or two against it.
People muzzle their dogs when they take them for walks, and there are no stray dogs or dogs without leashes. No more random dog attacks with helpless owners standing by telling you, "don't worry, he doesn't bite" ("70 percent of the time," they always forget to add).
Automobile emissions standards are tangibly better than in Ukraine, and car exhaust, while present, is not chokingly toxic, but merely insidiously unhealthful.
Finally, the people are not as dour, and seem more relaxed, trustful, and open to outsiders. There is almost -- believe it or not -- a sense of community.
On the other hand, Przemysl and the rest of Poland have wholly embraced the automobile lifestyle to the detriment of public transportation and pedestrian-friendly development. Ukrainian towns are more pedestrian friendly and have more street activity per capita. Depending on your point of view, this could be seen as a pro or a con, but considering the high likelihood that world oil production peaked permanently in 2008, Poland's recent vast investments in automobile infrastructure will probably turn out to be a complete waste of resources.
Photos of Przemysl (from two separate trips)