The Museum of Turkmen Values is a rather empty and overpriced look at traditional Turkmen clothing and jewellery. This is a popular spot for wedding groups to take photographs with a golden statue of the president, and the fountains are pleasant enough (a kind of totalitarian Waterworld, if you will).
The Monument to the Independence of Turkmenistan, known universally to the foreign community as 'the plunger' (for reasons obvious as soon as you see it), is a typically ostentatious and tasteless monument which houses the Museum.