With plums and apricots I put them on a table where they get some sun, if they are hard when I buy them. But sometimes they go to mushy very fast. We have good melons here, and some produce. Some local grown, but a lot from Mexico. Lots of pecans grown here.
Always brought back pecans from my BIL's place, if I didn't feel like shelling then I'd stick in the upright freezer.
A while back, cleaning it out, decided to get rid of the older ones, I'm the squirrel's best friend.
Fruit : try ripening by putting a few at a time in brown paper sack with an apple.