We spent a night at the Avalon hotel and liked it. From outside, the building is nothing to write home about - but it has been completely modernised inside and is quite trendy, with a great lobby area.
The rooms were clean and spacious, the bathrooms were less spacious but still modern and very clean. There was wireless internet which was great. The service was also good. We got the room + dinner meal deal, which meant that we had a dinner free, which was very welcome.
One of the positive points about this hotel is its great location just on the outskirts of the Old Town. This makes the Old Town easily accessible. However, the hotel is also a 3-minute walk from the bus station, which is great if you're going on to Tallinn, Vlinius, or another destination by bus.