Please take it with a grain of salt - as this is always the case with visas or entry, we can only speculate here. So you have two options:
Going without a visa. The UK Landing Card does not ask about prior convictions, and in my countless visits to UK I have never been asked any criminal history questions. Assuming you come as a genuine tourist, with a reasonable length of stay, this question might never pop up at all. There is however a risk to be refused entry, although - in my personal and totally ungrounded opinion - it is very unlikely. And see the bottom.
Obtaining a visa. This is more reliable, as obtaining the visa pretty much assures that you can enter UK. However there is also a risk to be refused the visa. Considering that your conviction happened then longer than ten years ago, included less than one year of prison stay and that you been straight since that, it is unlikely to have any severe impact.
There is also another option - you can fly to Dublin, Ireland (and depending on where are you in USA, it might be even cheaper than flying to London). From there you can fly to London, which would not be subject to passport control.
In any case, do not lie about your criminal record, but also do not volunteer this information unless asked.