American Airlines has ticket prices in low $500s for LAX to Tallinn, Estonia; Riga, Latvia; Vilnius, Lithuania and several cities in Poland for travel departures into early June, then mid-August to early December. There are even ticket prices around $567 for travel in July.
American Airlines tickets
LAX – New York JFK – Helsinki, Finland HEL – Riga, Latvia – HEL – JFK – LAX
LAX – San Jose SJC – London LHR – Krakow, Poland – Helsinki, Finland HEL – Chicago ORD – LAX