I used to keep a pair of shorts handy but any more I go to the back yard nude without bringing anything to cover. I haven't had any issue yet with neighbors looking over but who knows it could happen. It is my fenced property so I should be able to dress or undress as I feel.
I have found that the availability of cover nearby is proportional to the likelihood of being seen by someone who would take great offense to seeing me naked.
If I am at home, I am either inside where I can easily move out of view of the open window or door. If I am in my backyard, I am either out late at night under the cover of darkness, or have myself positions such that my grill, trees, etc. block the view from certain locations.
If I am in a much more public setting, I once again use something substantial to block the view from certain vantage points. I think the furthest I ventured away from cover was the morning I dropped my wife off at the airport for a trip, and on my way home stopped at a park. We had gotten 4-6 inches of new snow, and it was very early in the morning (just after sunrise), so I decided to visit the park on my way home. I was the first person in the park that day (no tracks in the snow), so I went to one of the picnic pavilions. I stopped by the bathrooms and undressed completely. Leaving everything in the bathroom, I then walked out about 30 feet into the snow, laid on my back and make a snow angel (while still naked), then walked back to the bathroom and went back to the bathroom to get dressed again before heading home. I I must admit that was very exciting, and very stupid.
My place is in the country and very private. I have a long driveway and the house is not visible to the main street. I have a gate code that only a few people know. I have been "surprised" a few times but I don't cover up. I had same UPS guy see me washing my truck naked and then a few days later see me laying in the sun. All he said was "cool tattoos"! LOL
We also live secluded. At the end of a dead-end road, with a 500 ft long driveway from the road. There are no houses near us. We have a sign on the driveway saying:
"Clothing Optional Here
You may see nudity"
Consequently, we don't worry about keeping cover nearby. If anyone reaches the door, they have been advised, and our phone numbers are at the bottom of the sign, so they can call if they need us dressed. So far, no one has called, and no one has complained.
No I do not keep anything handy, if I'm laying out I'm on a towel. As you can see in my profile pic my yard is private enough that I can be nude back there. As far as my gates, they can only be opened from the inside so no worries of someone walking in. My best friend does have the door code for the house. He usually calls first, but sometimes just drops by. He knows if my 2 cars are here and I don't answer, I'm in the yard doing something and he'll let himself in if he knows my wife isn't home. We've seen each other nude on numerous occasions over the past 25 years so no need to run or cover up.