The Playa Municipal, also known as Playa Coca Cola, is the closest beach to town, just over the bridge that leads to the road to Omoa [1]—either a US$2 taxi ride or a long hot walk from downtown. Unsurprisingly, it is neither clean nor particularly safe.
East of downtown (go to the Texaco refinery, take a right, and go to the end of the road) is Playa El Faro (Lighthouse Beach), which is not much better, though it does have a pleasingly windswept feel, and food and accommodation at the Costa Azul hotel.
Much nicer is Playa Cienaguita, west of the municipal beach. There are several hotels along this beach, as well as the city’s best seafood restaurant. Taxis to Cienaguita from Puerto Cortés [2] cost US$5.25, or take an Omoa bus and hop off at the sign for Hotel Playa (US$0.30).
From the turnoff to Hotel Playa, it’s a 10-minute walk up the road to the beach entrance. The hotels and beach at Cienaguita are usually packed on weekends with vacationers from San Pedro Sula [3] and completely deserted during the week.
Links:
[1] http://www.moon.com/destinations/honduras/the-north-coast/puerto-cortes/omoa
[2] http://www.moon.com/destinations/honduras/the-north-coast/puerto-cortes
[3] http://www.moon.com/destinations/honduras/central-honduras/san-pedro-sula