​Walk – usually with purpose

I’ll walk to/from the shop.

Stroll – with/without purpose

I’ll stroll to the shop/about/around the town.

Meander – usually without purpose

I’ll have a meander about/around the town 

Wander – usually without purpose

I’ll have a wander about/around the town.

Amble – with/without purpose

I’ll amble to the shop/about around the town.

Mooch – usually without purpose

I’ll mooch about/around the town.