Gorizia is a charming small city, right on the border with Slovenia. At one time Gorizia was the main town of the surrounding region but has been separated since 1945 when the international border ran through the eastern part of the city. Today there is a new town, Nova Gorica across the border on the Slovenian side. Since 2007 the two cities have effectively rejoined when Slovenia joined the Schengen zone ending the need for passport controls between the two countries.
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.
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).
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.
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.