The nearest airport is Riga International Airport, to the west of Riga itself.  The airport is well served by flights from several European cities.  Find out more at http://www.riga-airport.com/en/ 

Public transport between the airport and the city is not particularly plentiful, although some options are highlighted on the home page of the airport website.  

The simplest option is take a taxi from outside the airport.  We recommend that you take one of the green taxis operated by Baltic Taxis.  These can be found in a separate queue behind the other taxis that congregate in front of the terminal building.  They offer a fixed-fare policy into the city centre which is advertised on the Air Baltic website at http://www.airbaltic.com/public/baltic_taxi_vouchers.html .  This policy allows you to book your taxi before you arrive in Riga and to print out a prepaid voucher which you can give to your driver.  Up to four people can travel together on one voucher. 

Buses do operate from the airport to the city - the regular local bus service, route no. 22 - does the journey at a fraction of the taxi fare, but the nearest stop to the hotel is a good 15 minutes' walk away.  There is also a special Air Baltic bus into the city which calls at a number of the main hotels.  Unfortunately, there is no stop at the Albert Hotel and once again, the walk from the nearest bus stop will take you about 15 minutes.