visiting tourist sites on tour

There's almost always an easy solution--no need to worry! Each country and region will be different, so it's best to ask local advice. I find there's almost always some place to safely park a touring-equipped bicycle. Asian cities usually have bicycle parking areas with an attendant to watch over your gear. In Western cities you can ask at an attended car park or attended public restroom. If nothing can be found, you can usually get away with parking outside the window of a restaurant or shop where the bicycle will look as if it is being watched (I was warned not to do this by a local in southern Italy, however). At tourist sites, I usually get permission to park near or behind the ticket office or near a food/souvenir vendor. Hiding a bicycle in the bush is probably too risky; better to find someplace where it will be watched over. I think that camping gear is safer packed away on the bicycle unless the campsite is in a safe area.

Also, if your panniers have zippers, I highly recommend keeping rain covers over your panniers all the time. Twelve years ago in rural Turkey someone stole a shortwave radio out of a pannier (I later got the radio back), but haven't had a problem since I've kept the covers on. Also, try not to have loose stuff tied on your bicycle such as shoes, clothes, and pumps. On a related note, inflatable air mattresses also need to be tucked away inside the panniers--not so much as risk from theft as that sun exposure will crack the sealant.

When I was in Thailand, if I wanted to visit a museum I would ask the sheriff to look after my gear and bicycle, of course I also locked it, but it seems to be better to notice the staff-in-charge that this is my bicycle, not other's.

But to be frankly, sometimes I would just skip some less famous tourist sites along the way, because of the hassle... I know I shouldn't do it this way, but after cycling for a long time, I would rather skip something minor...

If I really want to visit something, I check into a local hotel and leave the bike in the room.

Same as #3. Rarely had problems with this.

Given that there are more than one of you, you can always opt to swap off going into the tourist site, while the other(s) relax(es) in the shade, watching the bikes. Sure, its not as romantic or idyllic, but its feasible for sites that are short visits (i.e. less than 2 hours to explore). For sites that are more intensive its nearly inconceivable that there is no hotel or guesthouse nearby, like within walking distance. Get a room.

In terms of going for a walk, I assume you mean a roadside trail or something like that, that's not near any towns or hotels. Well, you can always walk the bikes about 100 metres down the trail, turn into the bush at some sort of landmark, and hide the bikes in the bush. Other than that your options are limited...