If you can't wait to get to the beach, you might enjoy a trip to Mamaia Beach located 0.9 mi (1.4 km) from central Mamaia. If you want to continue walking by the waves, head to Tomis Beach and Myrtos Beach, both within a short walk.
Palace of the Parliament is just one of the places to see in Bucharest, so why not enjoy the other things to explore during your travels? You can seek out the local tours while in the area.