Translation:My dog sits next to me and watches television.
In this sentence this doesn't really work. It's a very defined sentence, the dog is actually sitting. So you lose information (on the position of the dog) when you translate to to be. I would only translate to to be when 'vague' forms of zitten are used, such as de hond zit te spelen (the dog is playing) or de hond zit de restjes op te eten (the dog is eating the left overs). You can recognise this other use of zitten because it is linked to things usually not done in a sitting position.