3-6 month sabbatical in Colombia - $500 per month ok?

$500 USD/month is around $1.5 million COP at today's exchange rate.  That's at the lower end of the earnings range for many people in Colombia, depending on their profession.  But they live on it.

You can get a rough idea of what the Colombians make monthly here:
http://www.tusalario.org/colombia/Porta … tu-salario

For instance a high-school teacher of math or information sciences with 15 years of experience averages $2.2M COP, a carpenter with 15 years of experience averages $1.6M COP, etc.

Popayán is going to be considerably cheaper than many other cities, but I don't know any exact figures.

Personally I would not want to live on any less than $1000 USD/month or about $3M COP/month, in Cali, which is pretty reasonably priced for many things, but that's just me - we've had posts from others who say that $500/month is adequate.

I suggest you look at the threads you can find here:
https://www.expat.com/forum/518-22-cost … ombia.html

OsageArcher gave you some good advice.  Basically you can do it if you can live in near poverty.  I lived in Cali for 6 months and I lived lower middle class and I probably spent over $1,000 per month when you factor in the cost of our furniture and appliances.  I rented a cheap unfurnished 2-bedroom for about $200 a month and that meant I had to spend 2 or 3 thousand to furnish it.  Not really a smart move, but we gave the furnishings to my wife's very poor parents when we left.  Maybe we could've sold them for $1,000 after 6 months.