I liked Hotel Neiburgs because you don't just get a room, you get a studio-style apartment, complete with kitchenette so you can cook up some Latvian dishes of your own. The space is large, luxurious and modern... and extremely artful, being housed in a beautiful Art Nouveau building.
Wait, it gets better. The hotel is not only in Riga's beautiful old town, within walking distance of most tourist attractions, but it is also on one of the quieter streets, reducing the chances of being kept awake by the more boisterous elements of the late-night Rigan revellers (and believe me, there are some). Oh, and then there's the price - really not as high as you'd expect for a fairly luxury hotel, I paid 108 Euros. It felt like an absolute bargain - and compared to what other hotels are charging in that area, it really is. Breakfast was pretty nice too!