Alexia is less than 100yds from the beach. The beach is a bit on the windy side, so be careful as you will not realise you are getting burnt.
The rooms in the Alexia are basic to say the least and it can be very noisy, but you don't go to Rhodes to stop in your room!!!
You can always hire a car and get down to Falariki's great beach during the day. Or a host of other great beaches along that side of the coast.
As has been said previous you are in the right spot for the night life
Have a great time
PS here is the link for the water park, it's brill. There's a free bus service to the park from Mandraki Harbour, which is about a 10 minute walk from the Alexia
http://www.water-park.gr/home.html