This is one of the rather easy trophies, therefore I will just tell you a location for each of the three activities.
Chop wood: Visit Hod in Riverwood. You can get a job from him to cut wood but if you just want to chop wood for the trophy. Go to the place where you first meet Gerdur (near
Hod's mill) and there is a chopping block. There is also a axe nearby for your chopping needs.
Mine ore: there are many mines throughout Skyrim. I suggest going to Embershard mine, just next to the guardian standing stones. In the mine you will find a pickaxe. After retrieving, just go to one of the ores in the wall and mine.
Cook food: Again there are many cooking stations throughout Skyrim. I suggest going to the one in the Bannered Mare in Whiterun. Speak to the Hulda and buy some ingredients to cook off her. Then use the cooking station to make the food.
Thanks for reading this guide and good luck!