Visit Gorizia castle, walk across the international border to admire the stunning train station in Nova Gorica and have a gamble in one of the casinos in the Slovenian part. Generally Gorizia is the more beautiful city but it can feel like a graveyard especially in the afternoons and at weekends when shops are closed (as is common throughout Italy). Nova Gorica is much more lively and although the town itself isn't beautiful, its surrounding countryside, hills and rivers are especially so.
There are regular trains from Venice (and Udine) taking around 2 hours. There are also regular trains from Trieste taking about 45 minutes. If arriving from Slovenia trains will arrive at Nova Gorica train station about 10 metres from the international border. Walk across the square into Italy and take the number 1 bus (cost 1 euro 3 cents) into the centre of Gorizia or Gorizia train station (10 minutes).
What to buy
As with most Italian cities you'll notice that shops tend to close for lunch and on Sundays (even though the neighbouring city's shops remain open taking away their trade). Nova Gorica isn't a cheap city but you will find that Slovene supermarkets have a greater variety of goods and that alcohol and cigarettes are cheaper in the Slovenian city.
Surprisingly Slovene isn't spoken much in Gorizia (unlike the towns which surround Trieste). However across the border in Nova Gorica you'll find many people who speak Slovene, Italian and English.