I have a post for long-term research in Mexico on a Fulbright, and I imagine it might be useful to some if I posted information regarding a short-term trip. My experience is in Spain and Mexico in historical archives, but I imagine that this information might help people going to the same countries doing non-historical research and perhaps for people going to other countries as well.

VISA:

You essentially do not need a visa for short trips if you do not plan on being employed.

Spain:

You can enter Spain visa-free for up to three months. I did a two month stay without any issues. Here is a link for Spain.

Mexico:

You can enter visa-free for up to six months. I have stayed as long as two months without a visa without any issues.

What You Need for Archives:

Spain:

Mexico:

Both Countries:

 

In sum, it is relatively simple to get into archives as long as you have a rough idea of what you are looking for and the proper documentation to get access. Short trips are great because you do not need a visa, which saves you time and money.