The town of Nyaung U is just 4km away from old Bagan. This once-sleepy town has been awakened by footfall of travelers and grown into a bustling traveler center, with the lively Nyaung U Market and some most significant pagodas and temples such as Shwezigon Pagoda and Htilominlo Temple.
The colorful Nyaung U Market is definitely a must-see. It is divided into different sections selling a variety of items and especially noteworthy, it includes a wet market. You can find almost everything from fresh fish, vegetables, handicrafts, to Myanmar sarong (locals call it "longyi"). Make sure to shop around and bargain.
The Nyaung U Market also offers a great chance to mingle with local people and know how they conduct their daily life. You will watch how crafters turn a block of plain wood into a work of art, smell the scent of local rice, encounter friendly people daubed with yellow face powder (local sunblock "thankaka") on cheeks, learn where the thankaka comes from, and see novice nuns from a monastery nearby collecting alms from local residents…Just take the time to take some good photos.
If you want to shop around the Nyaung U Market, this sample itinerary right fits the bill.