Rīga International Airport (Lidosta Rīga) is served by numerous European airlines, including easyJet, Ryanair, Aer Lingus, Lufthansa and Turkish Airlines as well as Latvia’s low-cost airBaltic (airbaltic.com). You can easily get to the city centre by taking bus #22 (€1) or a taxi, which should cost no more than €20.
Options for cross-border train travel are fairly limited, with connections to Moscow and St Petersburg, but not to Lithuania or Estonia. The train lines still exist, however, and services may be reinstated in future. Eurolines (eurolines-latvia.lv), LuxExpress (luxexpress.eu) and Ecolines (ecolines.net) offer frequent bus services linking Rīga with Tallinn, Vilnius and St Petersburg, among other international destinations.
A daily ferry service runs from the Rīga terminal to Stockholm, Sweden (tallinksilja.com); as well as daily from Ventspils to Nynäshamn, Sweden (60km from Stockholm).