West Palm Beach is a tourist area and therefore will have less cheap hotels than elsewhere, but also more. Try hotels such as Super 8, Motel 6, etc. Also try looking in locations not right on the beach or near popular attractions.
There are many different hotels in West Palm Beach, and I do not know what your budget is, but I will list some that I came across in my search. There is West Palm Beach Marriott - (561) 833-1234 Hyatt Place West Palm Beach/Downtown-(561) 655-1454 Hampton Inn West Palm Beach Hotel -(800) 290-9051
Some affordable beachfront hotels in Southern California with stunning ocean views and convenient beach access include Pacific Edge Hotel in Laguna Beach, Crystal Cove Beach Cottages in Newport Beach, and SeaCrest Oceanfront Hotel in Pismo Beach.
There are many hotels around the world that have Launderettes within them. They are pretty standard for example in Disney hotels, but other hotels such as the Palm Beach Hotel club in Spain have them too.
The big red hotel opposite of the beach this has about thousand rooms for $150 each
If I were you I would actually avoid West Palm Beach. I would lean more towards Palm Beach. They are within miles from each other. The separation between Palm Beach and West Palm is the Intercoastal Waterway. Palm Beach is much nicer. West Palm has a lot more crime. Also, in Palm Beach you actually have the beach! When ever I go to Palm Beach I go out at night to West Palm for nightlife and different restaurants. In Palm Beach you can shop on Worthe Ave, which is the Rodeo Drive of the east. Home to stores like, Louis Vuitton, Armani Exchange, Chanel, Gucci, and more. You can get great deals on hotels like the Breakers, Omhoy, Four Seasons, and Ritz on priceline.
Some very luxurious and highly rated hotesl in West Palm Beach near the ocean or marina include the Marriott Ocean Pointe and Palm Beach Shores. They are rated from three to five stars by the website TV Trip at this address: http://www.tvtrip.com/pnh1BFJg-hotels-near-riviera-beach-munic-marina.
Among the highly rated hotels in Destin are Henderson Park Inn on Scenic Highway 98, Candlewood Suites in Miramar Beach and Wingate by Wyndham on Palm Street.
Travelocity has some hotels that you can combine with the flights. Other travel sites such as Orbit, Kayak, and more are some reliable sites that you can look up affordable hotels.
The West Palm Beach Marriot does not have an arcade within the hotel grounds. It does however have heated outdoor pool as well as a fitness center with 24 hour access.
Gansevoort South Hotel and Spa, Miami Marriott Hotel Biscayne Bay, Royal Palm in South Beach are some of the hotels near the Dolphins Football Stadium
Some names of hotels in Cable Beach are: The Pearle of Cable Beach Resort, Oaks Cable Beach Sanctuary, and one other is the Pinctada Cable Beach Spa Resort.
Some cheap hotels in Thailand are the Lemon Garden, Rangsit Grand, Tratip Hotel, The Cocoon Patong and Pano Loch Palm Rooms. They are located in Nakhon Nayok,Ban Lan Dok Mai, Patong Beach and Kathu.