There are two ways to watch someone in an unnoticed manner. The first and most obvious one is to hide: stay in the shadows and out of the subjects line of sight. Reese is good at this but there's a difference between good and god-like, and most people get that prickle on the back of their neck when they're being watched like this.
The second method is to be obvious as all hell. The subjects see you, sure, but they stop thinking about you pretty quickly. Reese isn't as comfortable doing this, but he certainly can. And at least Finch's comments in his ear keep him from going absolutely crazy (crazier) as he's standing next to the door to the subject's storefront, dressed like Santa and ringing a bell for donations.
Given that he's dressed as Santa, he feels it is only appropriate that he spends some of his time thinking about gifts to give away. Or at least, one gift to give the one person he to whom he wants to give a gift. (He's not giving Fuscu a gift.)
Given that his credit cards and identity information all came from Finch, Reese can't exactly purchase anything in secret. Given that Finch also performs surveillance on the entire city, he doubts he could buy anything in secret even if he had a personal credit card not set up by Finch.
The options are to (a) not give him anything, which Finch probably expects and that makes it all the more important for Reese to not do, (b) to buy him something and have it not be a secret, which really takes away half the fun of giving it to begin with, or (c) steal something, which seems like the best idea, really, but leads to the inevitable question of what to steal and from whom.
The problem of who wants to kill a sweet little shop keeper gets resolved sooner than the problem of what to do about a Christmas present for Finch, but nicely it all works out.
The guy who wants the shopkeeper dead has a rather beautifully decorated office, with a tree and lights and actual boughs of holly.
The people he passes on his way back from completing the job all smile at him as he whistles Christmas carols, dressed as Santa Clause with a bag full of decorations and a tree over his shoulder.
It's too bad he can't actually sneak down the Chimney into Finch's place, but the front door works just as well. And the look on Finch's face when he comes down the next morning is absolutely priceless.