The Agamim hotel Eilat is a part of the Israeli Isrotel hotel chain, and is not one of the most hyped hotels in Eilat, Israel, but I actually think it is one of the best hotels in this town by the Red Sea. The rooms are very clean, and so is the rest of the hotel, and you can get rooms by the pool if you want (ask for it when you make your reservation if you can!) and the breakfast buffet is amazing.
The reason most people do not even consider the Agamim hotel Eilat is that it is not located in the city center, but it really does not take long to get into Eilat, so you can easily do that at any time you want, if you just have a car.
It takes around 10 minutes to walk to the beach from the hotel, but since the pool area is so nice, many people do not even do that.
The hotel has a spa with many different treatments, including several options for massages, that are well worth trying!