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 months.

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 Rules;

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.

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 months.

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 Rules;

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.