Both versions of the sentences above have equivalent meaning, and in fact don't even have a difference of nuance, other than the infinitive form being a little less casual.
To indicate you wish to do something now or soon, you use "would". Think of it as an implied question that you are answering.
Implied question: (What would you like to do?)
Your assertion: "I would like to watch TV (now)."
It's worth mentioning that there is slight difference in meaning between the word "like" in "I like to watch TV" and in "I would like to watch TV." In the former, "like" almost exactly means "enjoy" whereas in the latter, it sort of pairs up functionally with the word "would" and becomes less about a declaration of enjoyment and moreso an assertion of intent or preference; almost like "would like" has additional meaning than either word would have on their own.