You’re going to stick out as a tourist no matter what you wear. If sandals are your best walking shoes, wear them for sightseeing. Make sure you have a different pair of closed shoes for going out to dinner though. Even in non-posh places you’ll feel more at home with shoes instead of sandals.
For shorts and the like, the word to keep in mind is modest. As Pookah notes, don’t wear short shorts or skirts. Sleeveless shirts are also a bit too bare for some places. If you’re female, carry a large sheer scarf that can double as a shoulder drape or waist wrap for modesty.