I am writing a handwritten thank you letter to my professors who wrote the letter of recommendation for me, and I am also buying them a small gift because they really helped a lot throughout the application process. I'd love to deliver the letter and gift to them in person, but that's just not the option for me now. I am wondering will the professors receive my letter and gift if I mail them to their department in the university? or should I drop them off at the department reception?
You can definitely mail the letter and gift to the department. In fact, if the professor isn't on vacation/sabbatical/traveling etc, the receptionists are more likely than most to know where the professor is.
In my experience, there are letterboxes for everyone, so if your letter & gift are small the receptionists will put them in the letterbox; otherwise they'll email/call the professor and tell her there's a package for her.
Another important point to mention is that you should make sure that your gift is not too generous. Some universities have rules in place against personal gifts that exceed a certain monetary value (I think that in my university it's $100 or so). Anything more than that, and the professor will have to (a) report the gift to HR and (b) most likely won't get to keep it. These rules are in place to prevent academic misconduct, so I would really make sure that your idea of small fits university guidelines on what small means.
As Prof. Santa Claus said, just ask for their mailing address, or look it up online.
As a note for other readers, I would say that, at least in the US, many professors might find a small gift a little weird, depending on your relationship. Someone who has mentored you (like it sounds like they have) would be less unusual than someone who has just taught you in a few classes.