I made a day-trip to Riga yesterday and I was very impressed by the city.
Old Riga is listed on the Unesco World Heritage List and offers a lot of "Jugendstil" architecture houses, which I am quite fond of. The city centre is easily manageable on foot, but you can also participate to the numerous bus and walking tours departing from the Tourist Office.
Food is not a problem: Riga has a lot of restaurants (I recommend the Lido buffet restaurants that offer Latvian food at reasonable prices) as well as many trendy bars for the young and beautiful. Unfortunately prices now tend to be the same as in most Western European capitals.
Even Riga airport is now up to European standards. It is a modern and comfortable building with a lot of seating areas. Passport controls are quick and unbureaucratic. The easiest way to transfer to the city centre is to take Bus line no. 22. A ticket costs 0,30 LVL. Transfer time is around 40-60 minutes, as Riga's streets seem to be chronically jammed.