Staff at the Elizabete very quickly answered my query about how to get to the hotel.

Hotel is aproximately 20 km from airport. There are three possibilities how to get from airport to hotel.

1) By taxi. If You send us Your flight details, we can book a taxi for You. The taxi driver will expect You in airport with poster where will be written Your name. We can put airport taxi on Your hotel bill and it will cost 8 LVL per taxi (~11.50 EUR). And when You are cheking out You can buy the same voucher at the hotel for the same 8 LVL. It will take around 20 min to get with the taxi from airport to hotel

2) By shuttle bus. Near the airport there is going Air Baltic shuttle bus. The price for that is 3 LVL (~4.50 EUR) per person. You can say the driver Your hotel name and he will let You out near the hotel. It will take around 40 min to get from airport to hotel.

3) By Public Transport. It will cost 0.70 LVL (~1 EUR). The bus stop where You get in is near the airport, but the stop where You get out is Stockmann. The bus is going around 30-40 min deppending from traffic. And then it will take around 15 min to walk to hotel.

I have been told that Vincents is the best restaurant in Riga. I'm happy to splurge one night, and had a very quick response to my email query for a booking.