Battambang is small enough to walk, so the choice is between the riverfront grid where everything already is and the quieter edges you would trade for a tuk-tuk ride.
The riverside grid — Streets 1 to 3
The blocks between the Sangker and Psar Nat, where the French shophouses, most guesthouses and nearly all the restaurants and bars sit within a few hundred metres. Walkable after dark and the obvious choice for a short stay.
On top of Psar Nat
Right at the central market, which means dawn noise and the best cheap food in town at the same address. The cheapest beds are here and the bus offices are a few minutes away.
Wat Kor and the southern edge
About two kilometres south along the river, where old wooden Khmer houses and a few small guesthouses sit among fruit trees. Quiet and green, but you will want a bicycle or a tuk-tuk for every meal.
Pick somewhere with bicycles
The town is flat and compact but dull to walk in the middle of the day, and most of what is worth seeing sits a short flat ride outside it. A guesthouse that lends or rents bikes changes how much of Battambang you actually see.