The room was fairly basic, comfortable bed, desk, shower, no tub. I did not visit Dubrovnik for the beach scene and water sports, so can't evaluate quality of the beach (keep in mind that anywhere in Dubrovnik that you can get in the water qualifies as a "beach") but there is a "beach" about 10 or 15 minute downhill walk, the uphill return is longer.
The walk to old town from Hotel R is about 15 minutes, again downhill. Definitely do the city wall walk but go early or late because the mid-day sun is unforgiving and carry water. You can catch the number 4 bus back to the Hotel.
The Hotel staff was very friendly and informative as to where to go to eat and what to do. I had a problem with my booking and the Hotel owner worked out all the problems.
Some of the guide books I read on Dubrovnik suggested that the areas outside of the old city walls could be dangerous at night. These books need an update. My partner and I made the walk between Hotel R and old town several times at night. Dangerous? No! More like a walk in Disneyland, Orlando style.
If you want to visit Dubrovnik and not spend a lot of money but get a clean and comfortable room, you can't go wrong at Hotel R. The friendliness and helpful staff is a plus.
I also recommend the Sesame for dinner but make reservations. It is a bit pricey but a good value.