East towards Merv, Turkmenabat
Follow the main road going right from the museum and ask for directions to Merv. Say you want to walk. The highway is about a 45 min walk.
Just next to the museum there is a nice three storyed fountain that can be climped and slept in. Be aware, this is illegal as there is night curfew for tourists after 11
Merv is a very old historical city on the silk road. Most of it was destroyed by Genghis Khan. Can be hitched very easily, but there is not much to see with out a guide or a good guidebook. You can ask for a guide at the hotels, or wait for some tourists on a tour, and offer them 20 dollars to join them.