Mom can be found inside her diner on the east side of The Den. Talk to her about what's going on in town, and she'll ask you to deliver a meal to Smitty. Agree and head out to the west side.
You'll find Smitty in the junkyard on the far west end, past Lara's gang's house. Give him the meal and he'll trade you a stimpak. If you head back to Mom's, she'll offer you a meal that restores a few hit points. You can decline it and come back later if you're not in need at the moment.
It's possible to fail this mission, if you take too long (at least a day) Smitty will just go to Mom's. There's no penalty except missing out on a stimpak, some XP, and free food. It's possible to gain the XP anyway by talking to Smitty after this and selecting the correct dialog option.
Also, if you intend to finish this quest, do it immediately. The children will likely to steal your stuff. Also, Mom will not speak to you unless you bring the meal.