I had a fantastic stay at the Elizabete as well.
The bus I came in on (from Tallinn) stopped at the other one (i forget the name)
that's just down the street, it looked like a nice hotel as well.
But the Elizabete was just a 5-10min walk down the street from that one.
If you will be doing all walking both are not real far from the main areas I did walking only and did great. The one down the street from the Eliz (again cant remember name, sorry) was probably closer to the old town and park and the Eliz is closer to the train station and the mall/movie theater there and the main bus station. But its not a huge difference I did not think.
The only disappointment I had was I personally did not think Riga was all that interesting, at least compared to Tallinn which I liked much better. But the Eliz was fantastic

And the Lux express bus's in that region are fantastic as well.
** Radisson Blu Hotel Latvij is the name of the other one. Just found it. It did have a nice sky bar on like the 30th floor or something and theres a casino there. But if I were to go back I would stay at the Eliz and just visit the other one if I wanted a drink or hit the casino.