Shall we go sightseeing around town or something?

Literal

Town sightseeing [or-something-でも] do [question-か]?

~でもするか is a casual, masculine pattern for suggesting an activity on a whim: 'shall we do X or something?' The でも adds a tentative, 'might as well' quality. 町中見物 compounds 町中 (around town) with 見物 (sightseeing). Short and natural.