I had 4 wunderful days in Riga and also had time to travel a bit out of town. The best way to find buses and trains are on www.1188.lv
You will get information about both time and prices.
As an example here is a link for travelling from Riga to Sigulda by bus;
http://www.1188.lv/transport/bus/schedule?from=R%C4%ABgas++SAO&from-id=7083&to=Siguldas+AO&to-id=7846Edited: 2:24 pm, May 21, 2012