Darren
If you are happy with cheap and cheerful, you can't beat La Casona Del Patio Amarillo in Bogota. www.lacasonadelpatio.com
About $US25 will get you a double bed, a private shower and a TV with local stations. Its in a very safe part of town pretty close to good restaurants and shopping centres but a bit of a hike from La Candelaria and the Gold Museum (an area you probably wouldn't want to stay in anyway)I walk the streets at 2am in this part of Bogota without any concerns (although the locals think I am crazy).

As for Kuwait City, I think the safest place to stay would be La Casona Del Patio Amarillo in Bogota