Just from my research, Crowne Plaza seems to be one of the nicest in Downtown Jax, along with Hyatt and Omni. Plus the rooms looked fantastic, updated, etc. Also, went through Tripadvisor and looked at the reviews and it looked great and people seemed happy.
As far as water taxi, I see that it cuts across the river, so essentially instead of having to walk the two miles around the bridge and down to the stadium, you can catch it right below the hotel on the river and ferry across and be let off on the bank of the river near the stadium. However, I do not know how much it cost, when it operates, etc. I did see that it seems to just be pontoon boats.