You were in the UK last year as a short-term student, I assume you were admitted under Paragraph A57A of the rules, "Persons seeking to enter the UK for short-term study". You now want to enter the UK as a visitor.
Do I need to get any specific visa or is the fact that it is just a
vacation allow me to not need a visa?
U. S. Citizens to not require an entry clearance prior to arrival in the UK. They just 'show up' and have a landing interview. This is explained in Paragraph 23A of the Rules...
A person who is not a visa national and who is seeking leave to enter
on arrival in the United Kingdom for a period not exceeding 6 months
for a purpose for which prior entry clearance is not required under
these Rules may be granted such leave, for a period not exceeding 6
So it's OK.
We always advise visitors who are returning shortly after a previous visit to be careful to carry supporting documentation because there's always the possibility of running afoul of Paragraph 320 (1)...
the fact that entry is being sought for a purpose not covered by these
There are some removal cases in the archives here bearing this out. If your landing interview is successful, you will be admitted under Appendix V of the Rules.
That constitutes your answer along with all the relevant links.