The 'museum city' of Pereyaslav-Khmelnytsky was the hometown and stronghold of Cossack leader Bohdan Khmelnytsky, and also where he signed the infamous agreement accepting Russia's overlordship of Ukraine on 18 January 1654. Today the whole town, with its 23 museums, has been declared a historical preserve.
When Taras Shevchenko, Ukraine's national poet, died in 1861, his famous poem Zapovit (Testament) requested his fellow countryfolk bury him on a hill overlooking the great Dnipro River where, after rising up and liberating the land, they could 'freely, and with good intent, speak quietly of him'. Kaniv, 162km down the Dnipro from Kyiv, is the spot they chose.
Sheshory is a Hutsul valley village stretched endlessly along the fast-flowing Pystynka River. In fact, it's the river that's the main attraction here, with many opportunities for wading and plunging in the heat of summer. The most dramatic water features are the waterfalls, a loud and impressive sight after rain.
A simple day trip from Odesa, the 'White City on the Dnister' is an ordinary industrial port, but with an impressive Akkerman fortress built by Moldavians, Genoese and Turks in the 13th to 15th centuries. Today the castle is among Ukraine's largest and best preserved.
Among the villages in the Ukrainian Carpathians, Verkhovyna is probably the most gorgeously located (alongside tiny neighbour Kryvorivnya). It sits on a wide valley floor ringed by mountains; Mt Smotrych is just one peak visible from here. Verkhovyna boasts a private museum of Hutsul folk instruments.
There are a couple of interesting side trips from Vinnytsya, especially if you are interested in Jewish heritage sites. The village of Bratslav, 50km southeast of Vinnytsya, is where Rabbi Nachman lived and wrote most of his teachings before moving to Uman. Several of Nachman's disciples are buried in a shrine-like cemetery on a lovely hillside overlooking a river.
Shatsky National Nature Park
The Shatsky National Nature Park lies 160km northwest of Lutsk in the corner between Belarus and Poland, and has some 200 lakes, rivers and streams. However, while fascinating to scientists, Ukraine's wild 'Lake District' and its deep Lake Svityaz is a long way from appealing to all but the most adventurous of (camping and rafting) tourists.
With your own wheels, the most impressive day trip from Lviv is probably Pochayiv Monastery. However, it's too difficult to visit quickly on public transport, leaving the fairly low-key historical town of Zhovkva at the top of the list. Its cluster of pastel-coloured buildings, handful of impressive churches and city-wall remnants will happily occupy you for an hour or two.
Truskavets is an old-fashioned spa town that in another country and another time might have given the Czech Republic's celebrated spa town Karlovy Vary a run for its money. Unfortunately, that sort of rivalry is a long way off, but the town still makes a fun day trip from Lviv.
Dusty and crowded, Alushta is the second-largest resort on the southern coast, but it lacks a hint of Yalta's elegance. In fact, it epitomises all the worst things about post-Soviet recreation. The beaches are dumpy and the hotels are laughably overpriced. Perhaps the only reason to visit is an excellent hostel, which can serve as a base for exploring the Crimean mountains.