I went with my son last year and we had a great time. Most of the bars restaurants are around the main square and they are inexpensive and good value. If you enjoy a good steak then Whiskey in the Jar is the place to go. In the main square, good atmosphere, live music some nights. We booked a table there for our first night so you are not searching and unsure where to go to eat when you get there. You can book it on line, check it out, the steaks were excellent. We both had starters, steaks and drink, bottle of wine plus beers and total bill was about £40. You can eat for much less than this but this place was excellent. Look on line for beer halls they make a lot of their own beers, micro breweries which are well worth a visit and again just off the main square but easily found and all in walking distance. There is not an awful lot to do re attractions but the Zoo is really good and a short tram ride from the centre.
From the airport we took the bus to the centre which cost about £1 each. Takes about 20 minutes. Turn right when you leave airport terminal and you will find bus shelter approx 200 yards along. You need to buy a ticket from machine. Press English translation or ask bus driver for assistance which we did.
We are going to Riga in April so looking forward to that. Not been there before so if anyone has any tips that would be great. Enjoy your trip.